I like a lot of the changes suggested here. I'll probably nap the ones for Eldritch Knight and Arcane Trickster as while I don't think that they are weak, adding the option to pick two spell schools would open up more options for character diversity and be a good thing.
For myself, the changes are the following, at least what I can remember off the top of my head:
Berserker Barbarian: If they choose to frenzy, they make a DC 15 Constitution saving throw at the end of their rage or gain the exhaustion level. They also cannot die from levels of exhaustion caused by Frenzy, and remove one level of Exhaustion caused by Frenzy on each short rest.
Related: I house rule that Lesser Restoration can remove 1 level of Exhaustion and Greater Restoration instead removes all levels of it.
Trickery Cleric: I switch their 1st level stealth advantage feature with their second level Illusory Self thing gained at level 2. Basically they spend their Channel Divinity to grant advantage on Strealth to an ally and can do the illusion thing infinitely. Powerful, but still uses concentration slot to use.
Purple Dragon Knight/Banneret: I bump everything down in level so they gain Rallying Cry and Royal Enjoy at level 3 (it's now on par with Samurai), Inspiring Surge at level 7, Bulwark at 10th level, I gave them the Leadership ability from Hobgoblins/Knights monsters for their 15th level feature, and a second use of Second Wind at 15th level per short rest.
Additionally, I also have Rallying Cry be able to work even on unconcious people, and let Bulwark work on ANY save like Indomitable instead of just mental saves.
I've yet to figure out a solution to either the Sunsoul or Way of the Four Elements Monk (I've seen a few decent homebrew floating around online) because I've yet to have a player ask to play them. I've also toyed with allowing Barbarians to use rage 1/ short rest (with it being 2/short rest at some point and 3/short rest at another) but have not tested it and I tend to run 1-3 deadly+ encounters per day rather than the normal model.
Sorcerer and Ranger are both honorable mentions, though not subclasses, that I have a whole redo on. Basically for ranger I let players use either the PHB (with variants) or the Revised version and use the Revised ruleset for the Beastmaster (removing the 5th level ability if they go PHB version, or letting them opt to take Extra Attack instead of said feature). I have yet to give every ranger subclass spells sort of like gloom stalker and monster slayer, but I have considered it.
For sorcerer I give every origin a list of spells to pick from sort of like cleric domains (spells 1st-5th level), but make them pick one spell at each odd character level (1, 3, 5 etc.) from said list that they are capable of casting at that level. They eventually get all 10, but staggering it keeps the sorcerer from being a bit too front loaded. I also allow all the variants from the class variants thing for sorcerers (and pretty much any class for that matter), mostly relevant here is spell retraining on long rests.
Additionally, I give them:
1) One additional metamagic at 7th and 15th level.
1a) A new metamagic called Elemental Magic (like the one from the variant), though I allow them to spend a second point to make said spells deal necrotic, radiant, or psychic damage.
1b) I let careful spell basically negate all damage done to Cha mod creatures when applied. Powerful, but more fun. I've also been prone to let players count any object they wished to avoid damaging as a creature for this, and even spend additional points to negate more creatures, but admittedly that puts it over the top.
2) I give sorcerers a feature that let's them once per day on a short rest regain half their level of sorcery points.
3) I give them a choice between ritual casting or letting their own person count as a spell focus rather than needing one. Either way they also get quite a few ritual spells added to their spell list
4) Speaking of spell lists, I have a houserule where I basically allow any spell that fits the theme of a character to be learned or prepared so long as they do not go overboard and abuse said generosity. I've get to have a true problem and it's kind of dumb characters like blue dragon or storm sorcerers cannot get call lightning, as an example.
