Ah yes, Ryusei's path. Tengu is right, you can ignore the Gespys and Schultzwalds for the most part. Maybe one or two Mobility upgrades if they're getting shot down a lot.
Overall, Mobility is the most powerful stat to upgrade for Mechs, and Evade the most powerful for pilots. Even those who pilot super robots (Like the Grungst) can have a decent chance to dodge for most of the game, and by the latter half you're going to be hit by a lot things that can practically one shot you, making the speedy real robots a lot better to use.
If you can spare the cash, weapons are good to upgrade, but you can beat the game with minimal upgrades to them, I did the first time.
SP Regen and Mental are huge helps. Beyond that I try to get Hit & Away for the ranged types and especially battleships. In-Fight and Gunfight are also great on the right characters.
Also, if you don't care about Battle Masteries too much, there are some levels that are good for grinding with the game over trick. The trick is, that if you lose a mission and don't reset or turn off your GBA, you keep the money from it next time you play through it. You might keep the PP and exp too, I don't recall. And the trick doesn't work as well in a New Game+, but I might be confusing it with OG2, which you should also play if you can find it.