Be aware that many cruise lines increase fares for Christmas/Holiday/New Years cruises. High demand from families and those who can only get that particular time off from work. You may get more bang for the pound if you can schedule at another time. Is it important that the birthday celebration be onboard, or could the cruise be the present - to be taken later? Only you can answer that.
In addition, be sure that you know just what would be important to you for your cruise. How large a ship do you want? Do you want glitz or quiet elegance? Port intensive or days at sea? Luxury, upscale, mass-market? Figure out what is important in a vacation, and then look for the ship to meet that need. For example, you probably have your own priorities for a land vacation. Now, make a similar judgment about a sea-based vacation and go from there.
Above all....read and do research. There is a ship and itinerary for everyone; you just have to find it.