I have an axis, a hardtail MTB and a cobbled fixed gear and have commuted on all at one time or another. I also do some grocery shopping on varied terrain. My routes take roughly the same amount of time, but I can run any of them the quickest on the axis (no real relevation here). I live in CO and at times, the hills suck on the fixed gear, but it is nice to have multiple options. The MTB is the slowest in the quiver.

Run the dogs on the mtb with an occassional off road excursion (driving to trails to then ride isn't worth it given my limited time)
Ride the fixed for shorter rides, commutes or quick workouts (and on the rollers)
Ride the cross for multi terrain rides, hills, commutes, and family rides

For a commuter, I would think about a beater in the 50 - 200 hundred dollar range. (ebay, craigslist, goodwill, sal army has some steals) If it gets wet, trashed, etc. who cares. I'm looking for one myself, that can be kept at the park and ride.