I can confirm which upgrades actually affect your car, as for which ones don't, I'll tell you what I always tell everyone, if it makes you feel like you're going faster then maybe it is, but ultimately the best testing is the testing you do yourself and you should take a lot of rumours with a pinch of salt.
Armour is essential in a race because avoiding damage keeps your car fast and competitive throughout the length of the race.
Brakes are important for extra stopping power unless you are driving something with brakes that lock up a lot Ie; Brawler or Slamvan, in these cases consider using the 1st brake upgrade instead of the maximum upgrade as it makes it easier to feather the brake pedal (so to speak) and maintain a decent amount of traction under braking.
Engine, Transmission & Turbo upgrades not only increase the acceleration of your vehicle but also the vehicle's ability to reach it's maximum speed, never trust the in game stats because they are deceptive and don't tell the whole story.
Spoilers, yes they do add a decent amount of traction to your car, making cornering smoother and helping to battle snap oversteer, but more than that, increasing the traction stat helps apply braking force to the road under you and the same with acceleration forces, try it for yourself.
Suspension upgrades are harder to explain, it is up to you to determine which cars need suspension upgrades and which don't, if you are a 'curb booster' (I'll explain that one later) then stock suspension will probably benefit you more than a lowered car possibly could, but cars that tend to roll over in some corners might be better off with a lower centre of gravity so consider buying an upgrade.
Wheels, as a general rule a tyre with a chunkier sidewall (Offroad) will absorb bumps and curbs better than a smaller profile sidewall (High end) this is also useful for 'curb boosting' and is why you might encounter many of the racing crews using off roads as their main hot lapping tyre choice, and don't forget bulletproofs, they don't just deflect bullets, they also can't be punctured from burnouts.
Curb Boosting is an exploit within the game whereby you can mount and dismount curbs during a race for a slight boost in your engine revs and ultimately making you move faster in a straight line vs people who aren't using the curbs, this works differently depending on your car choice, for example the Zentorno will gain a larger boost from curbs than the Osiris. Curb boosting can be useful but also a problem for other racers on the track, weaving back and forth trying to grab curbs can cause you to take out other racers and knock down a lot of poles and debris in the middle of the race track. I would suggest avoiding over use of Curb boosting but instead try to use it mainly for 1 player hot lapping scenarios where you are trying to set a world record lap for example.
That concludes my life story, hope this helps some people