First off, there's really only 2 rules that must be followed in a Nuzlocke:
1. When a Pokemon faints, it dies
2. You can only catch the first Pokemon you encounter in an area.
Everything else is an add-on. From the hardcore rules you see all the time on youtube, to the weird and wonderful rulesets no sane man would challenge but people here do regularly, to simply nicknaming your Pokemon to get more attached. None of that is necessary.
And a lot of the more standard rules are, in fact, their own ways of making things easier! As an example, Dupes Clause (a rule where you do not have to catch a Pokemon of the same species you already have) was made probably because someone was just really tired of using rattata and pidgey, and nowadays it's more common to see runs with some variation of it than without. Same thing with something like Shiny Clause, which is literally just "shiny pokemon can be used because like. come on. it's a shiny"!
If you're worried about getting the run off the ground, let yourself ease into it - don't worry about your Pokemon fainting until you first get given Pokeballs. If you're worried about not being allowed items in battle or having to play on set mode, just leave those rules out. They can't hurt you if you are not bound to them. ...if you're worried about the emotional impact of your first death, I cannot help you there, I still feel remarkably bad about mine. You learn to live with it.
As for the "which game" question, I have like... No Experience with BD, but I know Omega Ruby is a game that functions so.
But genuinely though, OR might actually be a good pick for you! It has the early Exp Share (with the toggle that gets dropped in Gen 8), Infinite TMs, and I think a pretty good blend of easy & tough challenges.
In the end, however, just do what you want to do. We can't tell you how to play or what to do - it's your run.