Best Cpu Cooler For Around $50

1) Noctua NH-U12S

2) fans-> try pcpartpicker

For fans I'd suggest maybe non-variable 1000RPM fans as a rough guide. That's usually more than enough air pushed with the added benefit they don't ramp up when the system is turned on to a lot higher thus noisier (like an 800RPM to 1800RPM would even if fans never exceed 1000RPM).

My fans never go above 800RPM (i7-3770K + GTX680).
 
update:
1) Noctua was closer to $60 but I didn't see much for $50 that I could recommend (I'd spend the extra $15). Use this if comparing:
https://www.techpowerup.com/reviews/Noctua/NH-U12S/7.html

I setup a FAN PROFILE for my dad and so it sits at a completely silent 300RPM and idle and at 100% it's barely audible in a silent room (as the ONLY fan running in the computer).

2) Fans->
http://pcpartpicker.com/part/enermax-case-fan-uctb12nbl
or
http://pcpartpicker.com/part/bitfenix-case-fan-bfflpro12025brp
or
http://pcpartpicker.com/part/cougar-case-fan-cfd12hbb

*pay attention to dB especially (every 10dB is DOUBLE the noise so 30dB is 4X as loud as 10dB)