How can I tell what type of engine I have

Run your Vin on a web based decoder and you should be able to determine the engine code.

if the belt broke you have a very good chance that you did internal damage. take it to a shop and let them check to see if you bent any valves. Roy

Its written under your hood. Mine's a 2.0L SOHC for instance. If the timing belt broke, it could have just worn down, or something might have seized. It can tempting to fix everything yourself, but it might save you money in the long run to just check with a mechanic after (if) you replace the belt.