If it's this motherboard, then your upgrade options are rather limited: http://support.hp.com/lv-en/document/c01321559 What processor is installed (use CPU-Z or check in the OS if you don't know)?
Presuming it's the motherboard in the link, the fastest CPU should be the 65W Athlon 64 X2 5200+ P/N ADO5200IAA6CZ, available for as low as $2 on eBay and memory is limited to 4GB (2 x 2GB).
With such a low performance system, an entry level GPU is more than enough.
Not all video editing applications use GPU computing. As an example, After Effects, Premiere pro and CS6 can take advantage of NVidia Cuda or Windows OpenCL when using an AMD GPU.