Picking you opponent has the problem that people would just pick people weaker than themselves, and that online matchmaking would take much longer, as you would have to wait for people the same level as you to be available (as you wouldn't want to fight anyone stronger, and no one weaker would want to fight you).

As for the levels, there is your experience level (xplvl, and your matchmaking level (mmlvl).
The opponents you fight depend on your mmlvl, which depends on the level of the parts on your mech (items in the shop have their level below their name, your mmlvl is show near the bottom right in the shop).

If you don't add higher items to your mech, your mmlvl wont increase.

My advice is to not upgrade your mech every xplvl. Save your money up over, say, 3 xplvls, then upgrade your entire mech in one go.