When talking about hobbies transition into musical taste, from there it should be easy to bring up that you're a musician without sounding cocky. Have your guitar out whenever you bring her over to your place, or mention that you sing as well and she will probably want you to sing for her. At least in my experience (I've been playing for about 6 years as well).
As for style, it depends on the girl. My type of girl is punk/ska chicks, so normally I'm playing acoustic versions of punk/ska songs and singing for them, but some girls really like watching a guy shred on an electric.
From my experience, some panty melting songs to sing are: Substitute by Frank Turner, Love, Ire and Song by Frank Turner, I will follow you into the dark by Death cab for cutie, I miss you by Blink 182, and The lowly Carpenter by Mischief Brew.
Good luck man, us pick up musicians gotta stick together
