I would start with the piano (or electronic keyboard if no room for a piano). It's easy to learn if you have ANY musical talent, and you don't have to "toughen" your fingers as with many stringed instruments. You can work out whether you have the talents and interest to really get into music. Once you have the basics down (like reading sheet music) you can switch to another instrument if you want.
Guitar and drums are 2 really fun/cool instruments. Drums will be expensive, and guitar might be expensive but it kind of depends. It's really cool to just sit down one day and bust out a cool riff on guitar or beat on a drum and have fun with it.