Basement Ceiling - Take Out Old Popcorn Ceiling & Expose Rafters?

[Jesse Smith]

I own a 3-plex, which was converted from a large, old home (built in 1910, converted in the 1990's). The basement unit felt like a cave when I bought the place. Walls were brown, carpet was brown, and the ceiling is quite low.  It's a finished ceiling with popcorn over drywall, and it doesn't appear to be done very well.  You can see some discoloration and uneven spots.  Additionally, the ceiling fan hangs so low that I can almost hit my head on it.  

I've already removed the carpet and painted the walls white to brighten the space.  Now the ceiling looks dingy against the bright walls, and it feels very low.  I'm considering removing the ceiling to expose the rafters/ducts/pipes/wiring.  The plan would be to paint it all a single color.  This would also give the opportunity to replace low light fixtures with higher can lights.  I want to make it feel like a higher, more spacious area.

1. What should I look out for in this process?  Potential pitfalls?
2. What color should I paint the rafters/ducts/etc?  If the walls are bright white, would a dark ceiling make sense?
3. Would I need to re-run the wires, if they are crossing the main part of the ceiling?
4. Thoughts on flooring?

Thanks for the advice!

**First photo is from the original listing - The walls were MUCH darker than they appear.  First tenants also trashed the carpet, so it needed to be removed.