Yeah, Witcher 3 is the obvious choice. Unfortunately it basically is brand new; you'd be spending $60. But FWIW I loved the hell out of it and I didn't like Skyrim either (largely because the combat sucks). You could also pick up Dragon's Dogma: Dark Arisen for 360 or PS3. That can certainly be had for cheap.
No, they aren't on PS4, but I haven't played 1 or 2 either. There's plenty of backstory that gets brought up, but it's not that important to pick up on it and what is important you learn soon enough. The only point where it is an issue is that you get interrogated by a guy who brings up the previous games events. How you answer his questions can effect outcomes of the game (this is an overall part of the game that's pretty cool. Things you say and do have consequences). If you had played the game, you could import your save files. I just went online and read a primer about these questions so that I could decide what I would have done in the previous game had I played it. A friend of mine speaks highly Dragon Age Inquisition. But I've got a building backlog of games I need to get through before I try that myself, not to mention Mad Max is coming out in a couple of weeks and that will jump the line.
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Never purchased a DLC before, but this is going to be my first. Already put in over 110 hours into MGS 5 and I'm only 50% complete. I also have Nobunaga's Ambition that I want to sink my teeth into and I think Persona 5 is suppose to release this year?