I think limited Ammo would be fine, also gives you another item to worry about Inventory management with.
As for the Weapons, I got the feeling at the moment when I cycle through weapons it cycles through everything I got in the Inventory, I'd like to be able to place like 3 of the weapons in my Inventory on the belt (kinda like in DS with equipping multiple weapons, instead of going through your whole Inventory of weapons) and then when cycling it only goes through those three. If thats not the case, then it just autoequipped the weapons I pulled from the chest to the belt and I haven't found a way to access the belt. But I guess this is not really an issue if you have the "main" inventory be the chest, so you only really take out the Items you're currently wanna work with/can fit in your grid, since then I could only take with me the weapons I wanna use, and have the extra ones just stay in the chest. Then it also makes more Sense that its a rather small grid to work with, I was a bit worried on how you planned to fit 10 or 20 weapons in there at some point.