You should go with a 800w PSU $150.00
Since you will be streaming you need a elgato capture/stream card $162.00
For a motherboard go with ROG $250.00
A ROG Strix 2080ti will be your best bet for a GPU $1,350
Personaly I like the h700i case by NZXT $200.00
32gb of G.Skill 3000MHz. The rgb looks really nice $200.00
To go with the NZXT case go with NZXT Kraken x72 exelent cooling performance $200.00
Total: 2,992 (without tax)
Those parts are all good quality and witching your buget.
ps. what platform will you be streaming on. And good luck.