let me look in my karaoke files. lol! my b/f hosts karaoke and dj's so I got all his music...
I don't think you are gonna do what I do b/c I sing a lot of country and Pat Benetar..lol!
but popular ones done where I go to (one place is NOT country while the other is)
Picture-Kid rock duet
Hank Williams Jr. songs
Queen's Bohemian Raspidy (sp wrong I know)
Garth Brook's Friends in Low Places
oldies seem to be popular
Grease's Summer Love duet
all I can say is look thru the books and pick out something you feel most comfortable singing. Most KJ's can also adjust the key for you to fit your voice. Also do a lot of reverb on mics to help out too.
Most of all remember this: Karaoke is about having fun. Don't worry if you don't "sound like the original singer". Don't think that you are trying to just do a perfect cover song. It's about fun. The fun part IS listening to others sing and make a "hee haw" of themselves. and to think that you sounded better than that!

I do karaoke anywhere from 3-4 times a week.
Have fun!