I agree with Donna - find a reputable agent, preferably a Cruise Specialist, to work with. Their expertise can be invaluable in helping you find the best cruise for you.
Keep in mind when sailing out of NY that your first 1-1/2 days and your last 1-1/2 days will be sailing to and from the Bahamas. Unless you want to go for a longer time, you're going to be limited to the Bahamas and can't get to the Caribbean since it's too far away. The Bahamas won't be as warm and your choices are limited, unless of course you prefer to cruise to Canada/New England.
As for 'good price', that's a relative term. What's good for one is not necessarily good for another. It also depends on the 'single supplement' and whether a good one is being offered or not. And lastly, it'll also be based on the type of cabin you want.
Just some reasons why you need to discuss your plans with an agent who will help you find the best cruise based on your requirements, lifestyle, and budget.