I've ridden a mountain bike with slicks (my current ride) and also a road bike. Either one is OK, of course the handling will be different but I like them both just the same. The road bike had a more "sporty" feel to it whereas the mountain bike has a more "tank" like feel to it. Either one will be fine though and you'll have tons of fun. I would say pick the bike that fits you best!

As for gearing, go a tad bit higher than you normally would for single speed or geared. Climbing hills fixed will be quite an adjustment anyway....