Advice:
Don't buy or use the Monster Manual 1. Get the Monster Vault instead. It has many of the same monsters, updated with new Monster Math, and tokens, if you like them. The newer monsters are deadlier but generally not as tough, so they're not as grindy for PCs to defeat. The solos are also far better designed.
I could say the same thing about the Monster Manual II, in fact. It's not that great either.
On a similar math note, skill DCs have been updated. The first time I used the old ones in combat (PCs were 4th-level), they were being grappled. Noone could escape, as the old DCs were just too high. Made for a lame battle, although the rest of the battle was so cool the players still talk about it. These are in the errata files, the DMG2, and a bunch of newer books I can't remember off the top of my head.
Make sure players know how to fill in a character sheet by hand. Personally, I hate the Character Builder, but almost everyone else seems to love it. Putting that aside, it's pretty bad if a player doesn't know where the numbers on their sheet are coming from. I had to teach a player about this (since his character was a pregen built by the DM) and this player later became a DM... it's a good thing he knows this now. If players are using the CB (and they probably will), familiarize yourself with it too. There's all kinds of little issues with it, such as having four attack bonuses and damage values for each power, including illegal combos, that I've seen. (Familiarizing with the CB is an area where I need to take my own advice.)
1st-level heroes are much tougher in 4e than in any previous edition. They can withstand multiple encounters per day, and should be made to do so.
Don't use too many sources. What sources you use is up to you, but I'd start with the PH1 and Heroes of the Fallen Lands/Forgotten Kingdoms. You don't need to open up Heroes of Shadow (as an example) with its vampire class (yes, you read that right, class) and pointless assassin, or Heroes of the Feywild with its arguably overpowered pixie race, or the PH2 avenger class which ends up with a brokenly high AC score when it's using a PH3 feat designed for monks but open to everyone, etc.
Familiarize yourself with the math fix feats, which are usually called X expertise. The ones you really need are in the PH2 and the first Essentials book. I personally find the AC-boosting expertise feats to be a bad idea at heroic levels, as despite the consensus of the message boards I don't find PC AC to be lacking at all. (Their defenses, on the other hand...)
You
might want to use themes and backgrounds. These are optional, so don't feel pressured to do so. Themes are cool, IMO, because they give an extra encounter power at 1st-level. (Otherwise, you have players who feel their character can only be cool once per encounter...)
Use the errata. PH1 doesn't have that much crazy unbalanced stuff in it, but thinks like Blade Cascade and Destructive Salutation (stun on a
miss) needed fixing, and got it. Also, conjurations got an errata which they desperately needed, but there's not a lot of summoning in the core books.
Keep monster level near that of the PCs, at least at heroic levels. (I ran an 11th-level session for the first time yesterday, and found a solo monster three levels over the PCs isn't grindy at all.) If you think a clutch of 1st-level monsters and a 5th-level boss is a good idea, I would suggest turning that 5th-level monster into a 1st-level solo instead. Worth the same XP, but PCs won't keep missing it.
Do you like rituals? Some players love them, others hate them. Personally I love them, but I'm not a fan of spending gold pieces that could have gone toward buying new items instead. If you want PCs to use rituals, go easy on them. Consider reducing or even eliminating the gp costs (not healing surges, time, or other such costs) and don't be afraid to have NPCs use them too. They're a pretty cool way to put a stop to the 15 minute day problem, which is admittedly less of a problem in 4e than in 3rd. (If PCs decide to retreat, rest and fight on the next day, the NPCs can use rituals to help themselves. Picture the PCs walking a trap-filled hallway, now filled with Hallucinatory Items that NPCs can hide in. Or worse, if half the monsters in an area are just illusions. Just picture someone failing an Insight check and wasting a daily power on a figment.)
There's tons of advice sites out there. My favorites are probably Sly Flourish and Angry DM, which will also link you to numerous other sites. (Both have great advice for boss fights. One time I used both sets of advice, resulting in a really fun battle.)
Making monsters is so much easier in 4e than in any previous edition. I've committed to making 5th, 10th and 15th level versions of every PC class in the PH1, and I think I've done it too. (In many cases, I do multiple builds. So I have a 15th-level star, fey and infernal warlock.) Handy for when you need some NPCs right now. 4e doesn't have Paizo's excellent NPC Codex or equivalent, unfortunately, although to be fair, making an NPC in 4e is a lot less work.
Bonus note: Maybe it's just my players, but they're obsessed with having high AC scores. Most monster attacks are against AC. When making a monster, feel free to make some of their regular attacks against another defense instead (with a -2 penalty). For instance, a soldier NPC who uses a spear could have the attack changed to "armor-piercing spear" and have it attack Reflex instead, or a warhammer attack could become a "crushing warhammer" attack that targets Fortitude. Feel free to apply these modifiers to monsters you haven't designed. I do it!
I'm lukewarm toward some of the newer races (I don't really like dragonborn, for instance), but everyone will have different opinions. If you're going to limit races, let players know right away.
Take a steady hand in putting together a party. Not all the roles absolutely have to be filled (but if you notice no one is a leader, take a look at the healing powers; they're only minor actions so the cleric can still spend time on kicking posterior... clerics cannot be healbots unless they're pacifists, and that's something from Divine Power that a new player probably won't even see). Also, not 4e relevant at all, but a mistake I've seen better DMs than myself make, repeatedly, is to make sure the PCs all know and trust each other before the game starts.
There's advice on terrain and hazards all over the place. Use to spice up combat. I've found my PCs absolutely hate it when archers shoot them from rooftops. And by hate it, I mean the PCs start dropping! (Prone, and then often unconscious!)
