For folk and country music you need to play a harp in the same key. Blues players use the cross harp method to get the important notes as draw (suck) notes which are usually easier to bend to get that 'bluesy' sound.

This is the difference between playing 'blues harp' which is a term often used for a 10 hole diatonic harmonica, and 'blues harp' meaning playing blues on a harmonica. Your G harmonica will useful for songs in the key of G, so you could start to learn something you do in G first.

Good luck with your harmonica playing - it's lots of fun, especially if you don't have a moustache.