If you're just using it to commute you won't get a lot out of replacing the drivetrain. You'll just end up paying more to maintain it. Replace the drivetrain when it breaks.

New tires and hubs/wheelset are going to get you the most bang for your buck. If you can find a local wheel builder you can upgrade your wheelset for fairly cheap by buying a new hub, spokes, and rim. Better quality hubs will make your bike roll much faster and you'll notice it immediately. If you want to splash some cash or can't find a wheelbuilder you can buy a whole wheelset with better quality parts.

As for tires I would suggest something fast rolling like a Maxxis Pace or Ardent. That will have a little bit of tread in case you want to go roll on light trails but it will still roll really fast on pavement.

I would also suggest upgrading the handlebar and stem as that can also improve your comfort and maneuverability.