GPU temps are in the low 50s. Max I've seen is 56, looping superposition extreme as a stress test. Gaming stays lower, even in the most demanding titles.
$250 I honestly don't think is going to happen. Considering block and pump/res combo is about that.
Block and backplate(ek)- $180ish
Xspc photon x4 pump/res combo- $100(if I remember cost right, the d5 variant is $190)
Rad $50-80, depending on brand, size, etc.
Fans- up to $25 each x2or3. I got mine from performance pcs, with my rad, xspc brand, $28 for a 3 pack. Not the quietest but certainly not terrible. Imo a great balance between price, performance, and cost.
Don't forget fittings and tubing. I used, I believe mayhems clear soft, .50 a foot. So that's cheap at least, I bought ten feet and will have enough for another 2 builds. Fittings range from $2-10+ each, and you'll need at least 6.
Low end $350. My total cost was more, but includes two rads and a CPU block setup.