As with guitars, the F hole provides a more "punchy" sound, while the oval hole is more mellow. It depends what kind of playing you are doing, as has been mentioned. In a loud bluegrass group, yopu want the high, loud punch because the mandolin handles most of the percussion.

In a quieter, folky ensemble, or solo, The A-style would probably suit you more.

I've used both and can use either in either situation. But I usually use an Ovation electric-acoustic (that looks like a smaller version of their Adamas guitars. Acoustically, it sounds somewhere between an A- style and an F-style. Though I'm not a fan of the acoustic sound of Ovation guitars, the sound works pretty good for a mandolin. But where it really shines is when it's plugged in. It is a good match for my Guild/Fishman machine. The neck takes a bit of getting used to; it's fairly thick and wide for a mandolin, and the unison strings are a bit farther apart, so it's more of a chording instrument, though I do do a lot of picking on it.

If you feel like working with your hands, Stew-Mac has a few kits for building mandolins. The Campfire Mandolin kit looks interesting, but they also have an A-Style and an F-style kit for good prices.