I don't know why your choices would be between these four, they're all not very comparable, especially not the Wii compared to the others
I'd suggest getting a Wii and a PS3, most of the PS2's library is playable on either, either through direct ports to either system, or emulation/backwards compatibility on the PS3. This also covers exclusives on both systems, as well as Gamecube games that're playable on the Wii and PS1 games that're playable on the PS3 through backwards compatibility. The PS3 and 360 also share a significant chunk of their libraries; you'll be missing some exclusives that're only on the 360, but I'd argue it's not that big of a deal, unless you really wanna play Rumble Roses or Dead or Alive. (The PS3 also technically runs most games worse, but it's easier to softmod/install CFW on a PS3 and it also doesn't fucking kill itself like the 360 will)
The PS3's online store will still work until next July, so you can still download digital games and DLC (including PS1 and PS2 games that're on there) until then if you feel inclined, but something tells me you won't care for that.
Both a Wii and a PS3 should be cheap enough to get secondhand to where getting both shouldn't cost too much (My Wii costed ~$99, and I'm told it's easy to find one for way cheaper, and my PS3 was ~$170, and again, I'm told it's easy to find it even cheaper.)
Worth noting that the model you get for either console matters, moreso with the PS3 than the Wii.
With the Wii, avoid the Mini and Family models, as the Mini is missing Wi-Fi connectivity, and both the Mini and Family are missing Gamecube compatibility; basically, just get the first/original model.
The PS3 has several variations, and somebody else can probably explain this better than I can, but the original "fat" PS3 model has native PS2 backwards compatibility, at the cost of it having notable hardware defects (every fat PS3 will stop working at some point if you don't hardmod it); Every PS3 model is natively compatible with PS1 games. The Super Slim is missing native PS2 compatibility, but it's the most recent model, it's the cheapest secondhand, and it's less likely to succumb to fatal defects. I think the Super Slim is either difficult to softmod, or CFW on it didn't become feasible until recently (somebody else correct me on this if I'm wrong), but I know homebrew efforts for the Super Slim have gotten off the ground recently, so it should be possible to softmod sooner or later. Basically, I recommend the PS3 Super Slim model specifically, but you're free to pick and choose your poison yourself.
I want to pick up this call.
