The first question is if the chain is still skipping.

If the chain was stretched then your LBS should have told you that. Perhaps they did but advised you that a new chain would cause skipping. Even if it isn't skipping an out of spec chain is certainly going to eat what is left of that rear cartridge eventually. I guess it depends on how much you are going to ride it.

Adjusting the limit screws of the RD or even the cable (if need be) is a really simple job if the derailleur or hanger isn't bent. Your LBS should have seen this right off and told you about that.

I know you don't want to spend a lot of money on a bike, tools, or parts but I would suggest you get a book that will make working on them a cinch. Glenn's is very good and they are cheap as all get-out used. Look here and get yourself a copy for well under $10 with shipping -probably more like $5. It will take you step by step through even the most complex job and all you need to know how to do is read. I really encourage you learn a little bit more about wrenching if you want to ride and don't want to spend a lot of money on bikes (your LBS seems to be even more expensive than most.) If you do end up buying a walmart bike you are going to need to know even more about wrenching because they don't stay new very long and end up being even more work to keep up than a real bike like you have.