I live in Denver and I'm LDS and I served a mission, so I think I can comment. Although, we didn't use bikes in my mission.

I've also often wondered why missionaries are always riding mountain bikes, but after a lot of thought it makes sense to me. The deal is, that sometimes you have to be able to get ANYWHERE by bike, and on time for appointments. I can think of one example on my daily commute to work where I take the long way around on my road bike rather than go along a dirty trail. A mountain bike would be perfect.

Second, you have to get there and not be too sweaty. The granny gear on mountain bikes helps a lot. You will definitely not be in Denver your whole mission. You'll be in various places in Colorado, maybe even Grand Junction if I recall (I think the mission extends that far) or mountain cities.

Plus, as you said, you'll be locking the bike up outside A LOT. So you don't want a nice bike that's attractive to thieves. Having said all that, I really don't think you'll need a suspension fork. You'll have to go off the beaten path a bit but it's probably mostly just dirt, not mountain bike riding. You could get by with a cyclocross bike, although the drop bars might make it look expensive and be a mark to get stolen (different schools of thought on that). If you get a mountain bike I would go with a rigid fork. Disc brakes would be nice for bad weather. The missionaries around here try to get rides in the winter when the weather is really bad. You don't have room to be lugging around a spare set of non-foldable tires. I would recommend some kind of tires that aren't as aggressive as full MTB tires, maybe some cyclocross tires.

A hybrid bike might be ideal, if you can find one with disc brakes even better (I think Giant makes one). I'd put some cyclocross tires on your hybrid and call it good. Get a triple with low gearing and you'll be fine.