Great to know that you are planning Goa visit. Here are few points which could be useful for you -
1. Yes December is the peak season. Remember, you will enjoy most in peak season because it is Chistmas time and Goa will be buzzing with fun, parties and activity.
2. You are planning early. If you book now, you will easily get availability in any of the hotels within your budget.
3. You may refer to tripadvisor for hotel bookings.
4. You may also try OYO rooms which specializes in budget hotels and also offers great prices.
5. Goa is a great destination which attracts tourists from all around the world. It has beautiful beaches, churches to offer. It's a party place
All the best