Assuming we're talking about a browser game:
I think an inventory split into multiple categories would be better than an all-in-one inventory. It makes items easier to find (UX wise) plus I don't imagine it would take too long to implement as long as items are tagged with an item type. It would probably have more to do with how things are displayed on the page.
I definitely think an amount limit is necessary for any inventory system (I mean, integer overflow, right?) but I wouldn't know how to feel about weight limits. It can get a little hilarious when you have a hundred potions then couldn't pick up a, say, flower from a forest because of the weight limit.
I definitely agree with this, but I'm unsure how expansions should work with split inventories. I'm assuming by 'space', you mean slots, am I correct? You could have a limit as to the total number of item slots an account can have and allow the user to allocate their slots as they please, or you can have individual limits per item category, depending on how you want things to go.