I got a ATI R7 250 1GB DDR5 for about $39 bucks. Will this help out in my older 4 core Fx based computer with 8GB of memory--just for general use. It is currently running on the original NVIDA GeForce 8300 integrated GPU.
General use yes, very much so, and maybe even in gaming, Linux takes advantage of GPUs differently to Windows, the fact FOSS drivers are cleaner and are better optimized, they are like a fine wine, they only get better with age.
Dont expect to play Metro LL, but expect to play stuff like Don't starve and maybe even The Witcher 2 at decent settings :)