There is only one thing you can buy before a race, and it's not even an upgrade, because you are forced to as part of the shop tutorial. The rest are completely irrelevant at this time, other than deducting money from your app, until the next race is written. I'll be curious to see how upgrades will be handled.
I'm guessing they will unlock additional decisions to make during a race. The car is always shown at peak RPMs with the pedal to the floor. Traction, friction, weight, tires, and etc., don't seem to be tracked in the game as of yet. Unless races are changed: 1) shifting to the right gear in the ideal range; and 2) specific move decisions; are all that affect races.
Jake doesn't seem to have a full-time job, as he's getting his PhD. He's not a professor and says as much. I'm not sure what a guest lecturer gets paid in this game world... especially when the guy you report to hates you so much.