Try getting a credit card from the bank that you have account at. You can typically get a better rate/limit or even apply for a student card (which will give you a decent rate as well). I'm not sure if it makes a huge difference which card you get, but getting one with 0 APR as opposed to ANY APR seems like a better choice. Why pay the interest rate if you don't have to, right?
It doesn't necessarily damage you credit to cancel a card, but the more credit you have the better it looks (hence why it is not recommended to cancel cards with no balance).
You may be better off keeping the card after the 0% APR time is up, but then applying for a new card alongside that (perhaps keeping the first for only emergencies?). Running your credit score often can effect your credit (thus, applying for many credit cards very often can bring it down a tad), but in your case it doesn't sound very bad at all.
It sounds like a decent plan to me.
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So when you're happy (Hurray!), or sad (Aw!),
Or frightened (Eeek!), or mad (Rats!)
An interjection starts a sentence right.