I've used various types of chain. I don't like jewelry chain as it tends to be rounded links rather than squared.
Essentially you want chain to look similar to this

Whereas cheap jewelry chain tends to look like this

You can get jewelry chain that looks right but I've never found it at a price I'm willing to pay.
Small chain is available at hardware stores but they are generally made for strength and as such the shape is again usually different at small sizes. I found some suitable for putting on a vehicle once but never any that could be held in a figures hands.
The best source I've found is chain made for model ships. Anchor chains etc are enoumous so you're generally after the chains for smaller scales, which is good as they tend to be cheaper
