How to ya'll prevent smelling bad in the office after riding to work?
Some have showers at their work place, some shower at a gym close by, and some are okay with showering at home and just changing clothes with no shower, possibly using baby wipes or something else to clean off a bit.

Should I use my road bike or mountain bike to commute?
Depends on the terrain you will be riding on. Paved roads or bike paths = road. Gravel, dirt trail, other bumpy or uneven surface = mountain.

What type of bag do you use to carry clothing?
Some use a backpack, some use rear racks with trunk bags and/or side mounted panniers.

Any roads in the galleria/heights area that I should avoid?
I live in North Carolina. Can't help you here.

Lastly, any tips for beginners that you wish someone shared with you when you guys started commuting?
Try different things to find what works for you. Look through the forums here as there is a ton of good advice about what has worked for others. If you're thinking of doing this year round, you'll have to figure out lights for the shorter days, but starting right now that may not be much of an issue for a until fall.