The upgrade process mostly involves learning to fly the airplane from the left seat, with an emphasis on decision making and team building. First Officers at most airlines are already fully qualified in the airplane, so it is really just a matter of switching seats.
No matter what airplane or seat you go to, you always carry your system seniority with you. Now, that system seniority carries a lot more weight on the FO side than it does on the captain side, so most pilots take a hit in their relative seniority when they upgrade. Some pilots chose to wait until they can be rather senior captains to upgrade, some do it at the first possible opportunity.
Pilots can bid for new bases anytime there is a system bid, which is several times per year at my airlines. Of course, there has to be an open position to bid for.