Hi salparadise,
Welcome to SPCR!
On a budget I would try
Xigmatek S963 It’s low cost, light weight and, seems to me in my limited testing, very effective cooler. In UK its ~£15 and I don’t know of a more effective cooler for less! The larger S1283 isn’t much more money and maybe of interest if you want to overclock or have high ambient temps.
The minimum fan speed is 1200-1300rpm which is fairly quiet. If it’s not quiet enough for you I can recommend an
Arctic Cooling F9 PWM fan. It’s cheap, has good noise signature and runs down to ~600rpm which is very quiet and up to ~1800rpm that should be enough for almost any CPU with the S963. Don’t know about the fan on the S1283, there is an F12 PWM too though.
CoolerMaster Hyper 212 is also reported to be good and inexpensive.
Scythe PWM fans are reported to be good, come in 120mm and 92mm sizes.
If the PSU fan bothers you could try a fan swap, I’ve had good results with Noctua R8 (expensive), Sharkoon “golfballâ€