Okay, this is a dumb question, but I can't for the life of me figure out where the inventory or whatever is.  

Similarly, if there's a roster where I can just check out my current slavers, I can't find out how to get to it either. 

Left side of the game under end week. I don't think it's in the early early stage of the game, but there's an equipment link that'll bring up the armory. You make sets and equip the sets to individuals. Consumables are in the "item" tab link and bedchamber link is where you can set up bed chamber decoration.

Your slaver roster is in the same area where it says Slaver (#/#)