I've run games for decades...but no D&D since it was AD&D. I see a lot of sources to draw on for Class Options, Backgrounds, etc. Some fit well with what I'm looking for...but I was wondering if there were any that I should steer clear of -- ones that might be overpowered, unbalanced, or can cause problems. Are there sources you always go with? Sources you avoid? Specific elements?
It's all balanced just fine.
I'd suggest keeping it to the PHB to start with until PCs get to (say) 5th level, and then (once you're familiar with the rules) allow them to rebuild their PCs with all books open to them.
The most important class and encounter balancing tool in the game is how you run your 'adventuring days' - namely how many encounters the players get between short (and long) rests.
Long rest resources (spell slots, rages) are much more potent than short rest resources (superiority dice etc), and different classes get more from different types of rests, and different length adventuring days.
The game is (roughly) balanced around 6 or so encounters and 2 or so Short rests per Long rest (with a Long rest usually an overnight affair) as a median. Roughly 2 encounters per Short rest, and 6 encounters per Long rest.
Your first step as DM is to consider this and implement whatever rules or variants you need to ensure you hit this 6/2 per Long rest mark roughly 50 percent of the time (other 'adventuring days' can feature a single encounter, or a dozen encounters over multiple days with no chance to long rest, or more short rests per long rest or fewer).
You dont need rules for it; 'Doom clocks' are narrative tools that achieve the same thing. But there is also the 'Gritty realism' variant in the DMG that makes long resting much harder (and is appropriate for campaigns where the median is only 0-3 encounters in any one 24 hour period of game time - i.e. any campaigns away from dungeons).
Personally I use a rule that shortens Short rests to only 5 minutes long, but limits them to a max of 2 every Long rest, with at least 1 hour between rests. That way they're much easier to take, and less jarring for the narrative than 1 hour breaks in the action.
I do have a pretty 'dungeon heavy' campaign though so YMMV.
I honestly cant stress this enough though.
How you manage the 'adventuring day' and rest/ resource management of your players will affect balance more than any other decision you make as a DM. If you sit by and let players 'nova' and then long rest, classes will be totally out of balance, and encounters will turn into rocket tag as you ramp up the difficulty to match those nova tactics.