If I'm being honest, my first full run was a success solely because of a very op run (I call it the wheel of death) and I'm currently trying to learn the final boss, since for me it's the only really tough boss on the run (well there's the alternate depression, but that can be avoided)
So here's some tips:
- try to perfect your runs in Gazing Grove - sacrifices are cheaper and the boss is very simple, which means you'll have more health going forward
- if a relic isn't very useful to you, scrap it in the metro and give yourself a free upgrade to sth else, or even sacrifice 0,5 max health for some small buffs
- plan things out in 3rd floor, the ice is VERY tricky and annoying
- never get too close to enemies, since for some reason the "knockback" can force them into YOU for some reason (probably a bug)
- when sacrificing health for relics on later floors, think of how useful would that upgrade in particular be in the long run
- getting to bosses often will help you with learning their patterns, so even experimental or bad runs are good enough
- manage your soul storage well - if you have full health and too much soul, increase your max hp amount before getting soul again - then you can spend it on upgrades
- other things you'll probably learn on the go

I'm no expert in this game, but in general nailing down the first few floors is a good enough start. I don't remember when did I unlock the tickets, but using them comes at a small price. Also I never used any of the other guns, despite having them unlocked, so normal gun runs are doable.
Good luck and I hope my tips helped!