For that budget the 7xx series will be the best option. If you need 64 bit precision for calculations then that puts you in the Titan range ($1,000), but given your stated objective the 780 will be a good fit.If you are willing to spend a bit more then the 780 ti is the top dog, and worth the extra cash IMO.
If it’s just for leaning and prototyping at home I would get a Maxwell based one like the GTX 750 Ti. If it needs to be fast simply buy the fastest one, a GTX 780 Ti, and if you need faster double precision performance just get the Titan Black.