As far as dimensions go it is best to avoid multiples, especially the same each way. 12x13 is very nearly square. This room will have the same big bass modes L/R as F/R. The other room 10x20 is twice as long as wide which is less bad and also the extra length opens up some options. You could for example build a wall across one end shifting it to something like 10x17 cleverly using the space as both storage (component, records, etc) with the space behind as a bass trap. Mike Lavigne does something like this in his room. A guy could do worse.
Doing it this way the width is 17. Put the speakers on that wall, about 2 feet in and you sit a foot or two from the back wall. This gives you real wide space off to the side for awesome imaging and puts you about 7ft from the speakers for a nearfield experience that will require a lot less power. Especially since sitting near the back wall will give a lot of natural bass reinforcement.
Doing it this way the width is 17. Put the speakers on that wall, about 2 feet in and you sit a foot or two from the back wall. This gives you real wide space off to the side for awesome imaging and puts you about 7ft from the speakers for a nearfield experience that will require a lot less power. Especially since sitting near the back wall will give a lot of natural bass reinforcement.