Don't upgrade Gespensts or Shutzwalds - they're not worth it. When you get better robots, it's best to upgrade what they specialize in - armor for supers, evade for reals, energy for those that use a lot of energy. 1-2 steel knives and machines guns upgraded to the max will be very useful. For robots with set weaponry, it's generally best to invest in the strongest weapon, unless it's only a one-shot. Generally, if you have no idea what to spend your money on, it's best to save it rather than spend randomly.
As for skills, it's crucial to buy SP Regen for everyone as soon as possible - don't buy any other skills until you get this. After that, Attacker is a great choice, as well as upgrading Land/Air (depending on the mech the pilot is using) and Space to S. Offensive Support is good too, and SP Plus for pilots with supporting spirit skills.
Gah, I need to make a new comic soon, or my schedule will be worse than VG Cats'. And that's terrible.