Assuming your chain doesn't have a master link, you can cut it but will need to buy a link to close it again. As far as what chain to buy, there are lots of nice inexpensive 7s (or 8s is OK too) chains available, many of which have a reusable connecting link. Buy a middle range chain, spending more might save some weight but won't get you more chain life.

Before buying a link for your current chain, measure it for stretch using a 12" ruler. Here's a link for instructions how, and about chains in general. You'll find Sheldon Brown's site handy for other things too.