Here's a general overview of Metamagics, the hidden spells, the surprisingly powerful combos:
Careful Spell:
Everyone knows that save or suck spells work best for careful spell. Spells that require a save to prevent every bit of damage. Careful spells last as long as the spell does.
Although some spells like Otiluke's Resilient Sphere would make this redundant. (you either don't target your ally, and you wouldn't careful it for an enemy) there may be some very unique circumstances where it could be used. For example, if you simply wanted a large indestructible sphere but didn't want anything trapped inside.
'Wall' spells, which create a barrier, usually allow a save when it is first cast. Wall of Stone, when careful, allows the Sorcerer to entrap an enemy in a dome (Or Box) of stone, while allowing allies to automatically escape.
Mental saves are also very effective because they usually don't cause damage, and at least allow a full save.
Evard's Black Tentacles is a great choice. It allows allies to save for no damage or effect, and has a duration. It both damages and restrains each turn.
Guards and Wards could potentially be a great use of Careful because it contains a number of save or suck spells within it, that is if the DM rules. (Web, Stinking Cloud, Gust of Wind) I will probably need some clarification.
Tsunami has one save-for-half damage effect (6d10, yeah those commoners are dead...), then the rest is full saves, combined with movement control. Potentially causing suffocation due to drowning. It's a 300ft high wall, loses 50ft, after the first round 1d10 is subtracted from the damage. (This is not cumulative, so it's 5d10 -1d10, save for 0 on every turn for 6 turns, the point being that it's possibly to take no damage, even if you fail - rolling a 5 2s and roll a 10 on the minus)
Earthquake allows a Dex save to prevent falling damage and prevents the prone condition, as well as loss of concentration.
The Elemental Evil and SCAG spells provide some cantrips that can be effected by careful. Cantrips, being weak spells, allow for a save for no damage. (Sword Burst, Thunderclap)
They also contain a number of spells that use objects to harm targets (Catapult, Bones of the Earth, etc)
Maelstrom from EE targets a 30ft radius, halves their speed and pulls them toward the centre, while doing damage (6d6). Almost as powerful as Tsunami mentioned above. If they get knocked prone they are screwed. Avoiding allies with this is very useful, as they can gang up on creatures, knocking them over, gaining advantage.
There are many others but they are mostly covered by the PHB spells.
Distant Spell: (Edit: probably doesn't work like I think it does, making it a pretty meh choice)
With Distant spells there's the mediocre ability to reach creatures or things you wouldn't normally be able to reach, playing 'keep-away' with the enemy. You can buff allies in combat with touch spells, snipe enemies from long distances. It could be interpreted as a cousin to the Subtle metamagic, because enemies won't be able to detect effects from a very long distance, if they can't see you or hear you. These combinations aren't very interesting. There are some that make long distanced spells even longer.
However, there's the twist to this ability which is to extend the radial effect of a spell or 'Aura Effects'.
Some spells have a range of self, but in parentheses, there's an additional range. While there are other spells that have a range of self, but no other range, or it's mentioned in the body of the spell.
Magic Weapon is an interesting choice because it's normally used before battle. A wizard doesn't want to be in combat, fighting beside the front liners, so distant magic weapon, followed by a cantrip as an action.
Several of the Aura spells can be improved, doubling their range.
Aura of life targets people in a 30ft range, which can be increased to 60ft. It gives resistance to necrotic damage, hp can't be reduce and allies gain 1 hp if they have 0.
Leomund's Tiny hut can go from a 10ft radius to a 20ft radius, in case you have a large number of people with you. That 20ft feet into the air, 40ft from one end to the other. Pretty spacious.
Dimension Door. 500ft becomes 1000ft. Same for Arcane Gate (500ft isn't really that far).
Anti-life Shell. Now they can't get you with reach weapons because its been extended to 20ft. They can still shoot at you though...Same distance for Anti-magic field.
Paladin's Destructive Wave. Target everyone in a 60ft radius. 10d6 damage. Only targets enemies. Chance to prone them.
Divine Word. 30ft becomes 60ft. There's one problem. It says to choose any number of creatures within range, that you can see, but then also requires that they hear you. Still it's a massive range and the effects can take out armies. It's a bonus action, so you can use your action for something...thaumaturgy, make your voice boom?
Empowered Spell:
A lot easier for me to sort through. I won't recommend any specific spell because you should know the damage types already.
Obviously, the higher number of dice the better. If you roll below average on a dice. That's DIE divided by 2, re-roll it. The lower the number and the smaller the die size, means it's worth less. (no point in using it on magic missile)
People usually say 'But it's only going to make a 1/2 into a 3/4' You used a spell slot. The Job of a damage spell is to kill the enemy. If it didn't kill the enemy, it's not doing it's job. It's up to you to dice if it's worth a single sorcery point. Imagine rolling average 2s for your Fireball. Then the enemy gets to save for half. That's only 8 damage. Using empowered can boost it. Think of it as a modifier instead of a re-roll.
You'll want it for most of your higher level slots but you don't have to spend them unless you do badly rolling. Here's another check: A level 3 spell like fireball costs 5 Sorcery Points. A level 4 spell costs 6 (one SP more) sorcery points. If your Fireball does less damage than the average level 4 slot, re-roll.
Extended Spell:
Extended Spell is one of the more underestimated metamagics because most players don't see the difference between 1 hour versus 2 hours. I mean, if you can't get something done within the hour why bother?
The strongest aspect of extended spells is the ability to prepare ahead of time, particularly with spells that last a long time. An 8 hour spell like mage armour can be extended before taking a long rest. So, you don't require casting it again after you regain all your spell slots. This includes 9th level spells like Foresight. (should you ever reach such a level)
Effectively, a spell-caster (Particularly a Sorcerer) can have the effects of two 9th level slots at once. They can cast a mind-blank spell before taking a long rest, and then regain the slot in 8 hours. You can use up surplus Spell slots and Sorcery points, giving everyone in the party Darkvision, Mage Armour, Seeming, Creation Spell objects, etc.
The Aid spell is a good investment because it increases the Hit points of three party members for 8 hours. You can't stack a second one on though.
Or you can take a short rest and not have to worry about your hour long spells running out. After all, other classes like Fighters, Monks and Warlocks thrive on 1 hour short rests. A spell extended to two hours should mean 'You do a number of encounters, short rest, then another few encounters' effectively two hours.
Think 'Double'.
In this sense it is similar to the Twinned metamagic. Concentration spells are to be avoided, unless they involve specifically staying out of combat, say, you've charmed an enemy for a couple of hours.
Heightened Spell:
A very costly metamagic, but for certain high level spells, so worth it. Three levels of Sorcerer means a full caster can convert second and first level slots into Sorcery points to fuel this metamagic. Roughly six times.
You want to use it on your once per day spells. 6-9th level spells. That's 2 x 6th, 2 x 7th, 1 x 8th, 1 x 9th. Charm or Dominate spells with long durations should be very popular, and spells that only allow on save but continued effects.
Magic Jar is interesting because you create the Jar, you wait until you want to invade their body, and so they have disadvantage. Otherwise it would be a massive risk. They're immune for some time on a save, and they'll probably break the Jar or mess with your body.
Wall spells mentioned above in the Careful spell segment allow for a saving throw when you attempt to trap them, make sure they fail.
Glyph of Warding, Symbol and other spells that have the 'Until Dispelled' property allow you to create some potent Glyphs, hell you could even empower them. And they last as long as you need them!
Scrying. Compensates for knowing very little about the target. Literally, if his name gets dropped in conversation.
Otiluke's Freezing Sphere. Whenever you have spare time, start making them, Heighten them, empower them and give them to your friends as xmas gifts. It's basically storing magic.
Quickened:
Don't want to spend too long on this one.
You can cast a spell as a bonus action, instead of an action. Your free action is the interesting part of this metamagic. You can't cast another spell. But you can use your action to activate part of the spell already cast.
For example, Witchbolt allows you to use your action to cause 1d12 lightning damage.
Sunbeam allows you to create another beam, doing 6d8 damage, effectively doubling the damage and chance to blind.
A second use for Quickened metamagic is double cantrips.
Single cantrips are pretty weak. 2 Sorcery points for scaling damage (plus effects) is a bargain. It only costs as much as a first level spell. The special effects don't stack, so mix and match.
Three levels of Sorcerer would allow a spell-caster to quicken a Firebolt, then as an action Firebolt again, roughly 8 times, converting 1st through 2nd into Sorcery points.
Subtle Spell:
Every spell can be subtle. It adds and entirely new dimension to role-play other casters don't get. If you want you could be the embodiment of the 'strong silent type'.
Subtle metamagic adds stealth to the game that other classes don't get. DMs probably waive the rules when most spellcasters say they want to cast a spell when enemies are nearby. 'Oh I mutter it under my breath...' or 'I wave my hands like I'm dancing to music...' Sure they didn't notice.
You can cast most of your spells undercover when you are surrounded by enemies. You don't need to ask for a suspicious bathroom break.
Most Enchantment spells are good to subtle. They don't leave much of a trace.
Most non-damaging spells look cool when subtle. It makes your magic more mysterious because you don't have to make an ass of yourself with hand-waving and silly incantations. How much cooler were the Wizards in Harry Potter when they didn't say the spells out-loud? They just snap their fingers or point their wand, or maintain eye contact.
If you take Subtle, don't sweat it, every spell can be affected, so it's bound to come in useful.
Twinned Spell:
Strictest of all metamagics. One target that is a creature. No range of self. Requires sorcery points equal to the level of the slot, so you multi-classers need to keep it simple. No level 8 or 9 spells, unless you are casting Wish, and unless it's duplicating a spell lower than that.
Like extended spell it can be used to save spell slots for you and your party. It suffers from the same prejudices as well. It requires a different kind of thinking.
Obvious choices are single target damage (Blight Disintegrate), buffs (Greater Invisibility), de-buffs (Hex, strangely a bonus action).
Shield of faith. A very simple buff, you can cast it on yourself as a reward for casting it on your ally! In fact you should target yourself if it means you can maintain concentration on the spell for longer.
Heat Metal is already an unfair kind of spell, to be able to inflict it on two creatures is just mean. Again, not sure if the bonus action causes both targets to burn.
Vampiric Touch stands out as a rather powerful choice, although it requires two victims. You regain double the amount of hit points. Not sure if you can keep twinning on subsequent rounds.
Regenerate. It was already a powerful spell, now it's just double.
Simulacrum. It's kind of an odd spell. Target two people to copy. Creates snowmen of them, who have half the hitpoints but most of their abilities.
That pretty much covers it.
