Our partner gpuShack recently acquired a large stock of the R7950 Twin Frozr GPU, which measures 13.7db quieter and 10C colder than the reference HD 7950 model. While the GPU is already two years old, it is still faster than the R9 270X.
The GPU normally sells for $149. However, gpuShack is running an inventory clearance promotion at $5 off, and an additional $5 off with discount code SILENTPC, bringing it down to $139.
The R7950 Twin Frozr GPU is a great choice for a quiet budget build. You can pick it up at gpuShack while supplies last.