First, congratulations! Wonderful, exciting news.
Have you not spoken to this agent on the phone before? (You said you've done everything through email.)
If not, I would definitely talk with him/her before making a final decision to get a feel for his/her personality, working style, and enthusiasm for your project. Make sure you ask lots of questions about his/her plans for submitting your book, how he/she will keep you informed of responses, etc. I would also recommend contacting a couple of the agent's clients to see how they like working with this agent. And yes, ask to see a copy of the contract.
Hope this helps and best of luck.