Currently the game lets you do after defeating the final TRUE boss(not gasgoine) and activating the last lantern you have the option to save the completed file that gives you the next things for a new run of the game:
-it keeps the same character desing and it keeps the same path of stats as you picked but you are reset to level 10/4.
-you are given a list from the weapons you have picked(if they are upgraded its counted) and you can take ONE of them for the new run and you will have it inmediatly in your inventory.
-you are given a list of your clothes and items(including key items) and you can keep ONE of them for the new run(same as before you have it inmediatly in your inventory)
with weapons there isnt much to talk is just pick the weapon you wanna start with and you can maybe upgrade it beforehand.
with items... lets be real majority of the time its gona be the Basement key(get +5 weapon much early and some arcane items) or sewer key(get go gasgoine faster) or Dev key(get everything fast)