Howdy-
As preface, I am an old school 1E grognard that still has not shaken those particular habits off of my current 5E games. I also really like how 5E really has much in common with 1E, ease of character generation and a good system in general. I tried to get back into 3,5 earlier this year, but it was just a bit much to really DM. Skipped over 4E since it was not D&D, only in name.
So with that said, as an old grog, I really do not like the way some races and classes are presented in D&D, thankfully I can nix certain races and classes without effecting the system in general. So here is a list of what I disallow in my campaigns and why:
Dragonborne- Really? A munchkin gamers wet dream race come true, and a DM's nightmare on how to handle such a race in their campaigns. These are monsters after all, not heroic core race types.
Tiefling- Gee, really? really? Why on gawds green earth would a demonic creature such as tiefling want to be among-st the prime plane rabble? Another Munchkin gamers dream race come true lol.
Warlock- OMG shades of WoW lol! I nixed this class right off the bat, pacts just do not jive with my campaigns personally and seems better suited as a class for villainous NPC's.
Paladin- I did not nix this class but went old school. The artwork in the PHB for the pally is so wrong on so many levels lol. So what I did do with this class was just make it for Humans only, Lawfull Good and Oathbreakers are N/A.
Do I use the optional stuff from UA online stuff? That is pretty much a case by case situation. I do allow the Gunslinger, one of my personal favorite classes in my campaigns. So I am not all old school all the time lol.
As I said upstream, 5E is probably the best version of D&D I have played, not too complicated, not too simple, it hits that sweet spot for RPG's just right.
Scott
My Forgotten Realms campaign has been going for decades, and I still stick with AD&D style mix of PC and NPC races and classes.
For PCs:
Elves - Gold, Moon, and Wood - no drow
Dwarves - Shield (maybe gold, but quite rare)
Halflings - Lightfoot and Strongheart
Half-elves - no half-drow
Human (my players all have at least 3 characters, and 2 out of 3 must be human)
Bard
Cleric
Fighter
Paladin
Ranger
Rogue
Sorcerer
Wizard
Barbarians, druids, and warlocks (witches) are NPC classes, as are some archetypes. Monks are more of a western variety, although I haven't bothered with a class yet. Think Friar Tuck with simple bludgeoning weapons, no armor, wrestling and boxing, with some spellcasting. If it comes together well, it might be available as a PC class, but I'm guessing it won't be powerful enough for most to consider.
No dragonborn at all, well at least not like the PHB one. Humans and elves can have draconic ancestry (from a male shape-changed metallic dragon, and a female human or elf), and there are those that have fiendish (tiefling) or celestial (aasimar) heritage, but they appear to be whatever their base race is, and have different abilities. Some have more than others (which indicates how far removed they are from their unusual heritage). Many humans have traits that indicate they must have some exotic heritage, but can't determine what it is since it's so far back.
I'm very happy with the 5e framework, but have made a lot of changes to make it more like AD&D and my own preferences. So even my races and classes have changes, some minor, some significant.