And record what you sing, and be realistic when you hear it played back...

Don't worry TOO much about pitch (you can improve that!), but have a listen to your voice's timbre and 'sound'. You are FAR better off choosing material that flatters the voice you DO have, than picking songs you would PREFER to perform, but just don't work well with your range and timbre.

A vocal coach can help you develop a particular sound (but only to a certain extent), but basically, you are born with a certain type of vocal apparatus, that will sound a certain way. If that apparatus sounds better on country than jazz, that's probably the best material to use it on!

Now that is an extreme example, but you AND your audience will probably be happier in the long run if you find out quickly what type of music you sing best, and stick mostly to that!