Something like the Peerless Assassin is $35 I think, and will definitely keep the chip cool. I mean, if you like the liquid cooler by all means go for it too, its personal preference. But if I'm on a strict budget I would always pick GPU power...
Looks pretty good to me, although the liquid cooler is a bit superfluous. The 7800X3D doesn't run that hot, you could get a $30-40 air cooler and grab a 7900GRE instead. Just my .02.
I have. PC part picker list.
https://pcpartpicker.com/user/neek415/saved/yyK2rH
I found the same monitor for $149 instead of $250
Power supply $60 instead $84.99
Case $79.99 instead of $99.99
GPU for $489.99 instead of 519.99
SSD for $120 instead...
I'm pretty sure Im going to be able to grab a 7800x3d, I was able to cut some costs on my rig by almost $300 so I'm probably going to use those savings towards the CPU.