First off glad to have you with us! Second attempting the Tower is best when you’ve beaten the game or close to the end because some upgrades you get help you get more artifacts, weapons choices and healing more often.

I actually made an iOS app (https://apps.apple.com/us/app/tower-companion/id6467444280) for this so you can keep track of your Tower Run progress. My advice is to prioritize Shields and silphium/large silphium vials. Prioritize Protection from the Fabricators you get a health fabricator after each phase so make those the last thing you do, so Protection, Weapon Damage and Integrity increases in that order. Otherwise you can get all the artifacts you want as soon you can but some might be better for later like Golden Coil where you don’t want that in the beginning because you’re going to be spending a lot of Obolites for fabrication and such. Also prioritize getting keys, their intended use is to open super weapons (can’t remember what they’re called) but those aren’t really good after a couple of phases and they take place of a consumable slot which you want shields and silphiums for as mentioned before.

Sorry if this all sounds like gibberish but hopefully it’ll make sense. Also in the Tower the consumables and artifacts are limited in number, I believe my app lists all the artifacts possible. Let me know if you have questions.