Have you thought about keeping your Honda for a few more years? Is your car in good working conditions?
Hondas are great cars and go on forever. If it's all paid off, why go back into debt when you don't have to?
If you can hold onto it for a couple of more years, why don't you pretend you have a car payment to make, and put that aside in a money market account. Then.. you'll have a nice down payment.
If you're dead set on buying another car, here's a great website which gives great advice on the process... and should answer most if not all of your questions.
http://www.edmunds.com/caradvice.html
Two grand isn't much to put down on a new car... which means your monthly payments are going to be high.
As far as financing.. do you know your FICO score? If not, you need to! Get your financing from the bank... definately. Shop around.
Don't trade in your car, sell it privately.. you'll get more for it. Here's a site to find out what it's worth:
http://www.kbb.com/
Remember that cars are lousy investments. They devaluate from the moment you drive off the lot.
Good luck, whatever you decide!