According to this post, these are the rewards you get:
XP gain is always 5% of the cash gain.
CC gain is always one millionth of the cash gain
Loot drop gain is always half of the CC gain
There is approximately one cosmetic card earned per 100 SP.
For clarity, "CC" means continental coins, and "SP" means Spree Points.
This part of the reddit post I quoted is mostly correct. Only thing I can find wrong with that part of the post is that I got to a crime spree of 500 and actually got 7 cosmetic items instead of 5. That's probably why the post says approximately one card per 100 SP.
Cosmetic cards are always armor skins, until you unlock all armor skins that you can get from crime sprees alone. After you unlock all those armor skins, you get 6 continental coins on the next cosmetic card you obtain. After that, cosmetic cards give you even more coins, or none at all. I haven't gotten duplicate armor skins, so it seems you're guaranteed to always get an armor skin you don't already have.
I believe the cash payout you get from each heist depends on the heist and your catch-up bonus (if playing with a host with a crime spree 20 spree points ahead of yours).