Your other choice is a Vita. They are not good, though. Easily the worst iterations of their respective games. That said, the Vita versions did improve on them in various ways.
playstation now is an option, but since it's a streaming service and naturally kinda laggy i wouldn't recommend it. playing ninja gaiden with lag is the worst
The PS3 versions of Sigma are better. Ninja Gaiden Sigma & Sigma 2 are fantastic and well worth playing. The Vita version of Sigma 2 is a laggy mess however.
And it wasn't, but they implemented it later, and is not even backwards compatibility, they're just porting xbox 360 games to xbox one, which is great. Right now, PS4 doesn't run ps3 discs, digital ps3 games can't be downloaded on ps4.