In the reserves, you will normally do your drills (the 1 weekend per month) at the nearest reserve center (they're called Operational Support Centers now.) You will be assigned to a unit that has an active duty counterpart called a "gaining command". You will usually go to your gaining command for your annual training (that's the 2 weeks per year part.) If you move, you can affiliate with another center close to your new home. The staff at the center will let you know how to do that, paperwork wise.
yes. all travel is on you to get to and from drill. occassionally you can get lodging reimbursed when you are forced to drill in a location more than X number of miles away.. but if you CHOOSE to drill in TX while living on Guam.. expect it to be all out of pcoket.