I know that I'm late to the party, but I recommend stockpiling items and having very little cash on hand. As far as I can tell there's no inventory limit and you can sell stuff to Alyssa pretty much whenever. The result is that whenever you need to spend $X, you just sell $X worth of stuff and get the thing.
As far as I know the doll and the memberships are the really big things to get, and then the dungeon dweller has some useful items related to the dungeon as well as some tasteful dildos. Hope this helps.