So the progression is for each mech?
Partially. Each 'Mech tree lets you unlock minor stuff like slight bonuses to lock-on time, weapon convergence speed, etc. but also modules that are "programs" that enable sidegrades like improving night vision at the cost of it blurring more when you get hit. Modules can be used on any 'Mech once you've unlocked them. In addition, you have a pilot talent tree that grants generic bonuses, but again, they're small and just serve to customize your playstyle a little.
The only real factor getting new 'Mechs is simply how many credits they cost, and the prices vary pretty wildly. (1-3 million C-bills for a Light, upwards of 11 million for an Assault.) I don't need to play Light 'Mechs for 50 hours before I can buy a Medium.