How would an Nvidia gtx 580 card work with a 480 dedicated physx card? Would this encounter any problems with everyday tasks, or gaming (specifically crysis 3)?
Are there any better solutions for such a budget? (around 250-300 pounds total)
Don't do it. You will only make your system noisy and power hungry. The GTX 580 is good enough on its own, and a game like Crysis 3 doesn't use PhysX anyway, so the dedicated 480 would be sitting there making noise, producing heat, and using power for no reason. If you must have a dedicated PhysX card, something like a GTX 460 would be much better.
First, you need to ask yourself which PhysX games you intend to play. Often people get confused and don't realize which games support GPU-accelerated PhysX. The current/recent list is: Borderlands 2, Hawken, Planetside 2, ARMA 3, Lost Planet 2 & 3, Batman: Arkham series, Mafia 2, Metro 2033, Metro Last Light, and my favorite, Unreal Tournament 3. Of course there are several less popular titles as well and a few pending releases. https://en.wikipedia.org/wiki/List_of_games_with_hardwa...