You're asking what to do with $500 of budget. Things like brakes, safety gear, fuel system, driver education, etc do not fall into that category. They are all wonderful and smart things to do, but they don't need to be weighed against that $500.
I've never seen a team get sweated over replacing belts and hoses. They would much rather you not split a radiator hose and then require a tow. Same with belts. You aren't making the car faster with those parts. Where that changes is when you get into non-stock parts. OEM radiator with new hoses? not gonna get asked about it. Afermarket huge expensive all aluminum radiator with fancy silicone hoses and an accusump? They might start looking closer at things.
In my own opinion, if you're building a new car, priorities are as follows
1. Overall reliability. Replace old hoses, crusty water pumps, clogged radiators, cracking old wires, etc. Stuff that will take you out of the race when you start stressing it in a race environment. A bunch of these I wouldn't even count in the budget for reasons listed above.
2. Things that help engine longevity. Big oil cooler, bigger radiator, oiling system upgrades, stuff like that.
3. Suspension. going around a corner helps more than going fast in a straight line. Replace worn out shocks, get performance stuff if it exists in budget.
4. Go fast parts. Last priority, it will only make you less reliable.
20+ Time Loser
FutilityMotorsport Abandoned E36 Build2008 Saab 9-5Aero WagonRetired -
1989 Dodge Daytona Shelby 2011-2015 "Lifetime Award for Lack of Achievement" IOE, 3X I got screwed, Organizer's Choice