As is most things, it's seniority driven. The most senior in your class will begin and finish training first and they will also be the first people assigned with any Captains in upgrade training. If they run out of upgrading pilots then they go by seniority and assign hew hires to each other. Whether that happens is all dependent on the training demands at the time they create your sim schedule.

My sim partner was in my class and was an all-military background. He had the 737 type while I had all the 121 experience between the two of us. We worked well together. One key to 121 flying is always staying ahead of the airplane and operation. In the sim I've always been well served by telling myself if I'm sitting around doing nothing then I'm doing something wrong. The lessons are fast-paced most of the time so you'll be moving on to new tasks frequently. It's really something you have to experience to understand. I applaud your eagerness and curiosity but, even though I have no military service, I know you'll be well served by your training experience during your service.