Post preview:I remember to have had lots of fun with the Spyro games when I was a kid. Don't know for how much they go these days, but they might be the right thing if you're looking for something relaxing to play.
Cotton 2 looks interesting. I could use a shmup that has flying which instead of a plane or spaceship ;)
There are tons of games these days where you play some sort of character instead of a plane. You might want to check out Cave. Though I think not too many of their more recent games are available for mame.
Post preview:Well, then you have pretty much countless possibitlies. And countless annoyances as well, since you need to have the right mame version for each game. They won't all run on one version.
I recommend checking this out. It's what I used for getting started too. Most, if not all of these, should be available for mame as well.