I'll vote for the road bike as well unless you can find a steel MTB frame with horizontal dropouts (steel can easily be respaced to match a narrower fixed hub) in which case it's a toss-up.

Gear ratios are all relative to tire size. Gear inches are a much better measurement, but they technically will be relative to crank length if you are really anal. Gain ratios are the answer, but I find them to be a bit of a weird measurement to work with. I talk in gear inches for this reason.

If it's just kind of hilly, like 6% grades or less in most places that aren't too long overall, aim for the low 70s. If you have more hills and more steep ones, aim for the high 60s. I wouldn't go much lower than about 65 gear inches or you will be spinning hardcore. 68 or 70 would be a good ballpark to start with. Here's how to do the math: http://www.basementfreaks.com/members/karl/gearing/

Have fun with it and don't fall for the idea that brakeless is a good idea (especially in hilly areas). If you want to run brakeless, ride with a brake for at least a few months beforehand so you have a safety net while learning what it takes to control the bike with your feet. I ride a fixed gear road bike conversion almost everywhere I ride these days, and I run a front brake. I'm running 74.2 gear inches (48/17) with 700x23 tires and 165mm cranks, for the record. I can hit 38mph on good downhills, but it means spinning 172rpm of cadence (this happened yesterday, and twice recently I hit my previous record of 37mph/167rpm).