I'm strictly comparing the Wii to the Playstation 3. I'm very aware most of those games are on the PC and 360.
Here's the thing: there are a LOT of Wii games which you can't get on the PS3, 360 or PC and the only other way to play them is through obtaining the ISO in "some way" coughpirating coughnone of those torrents have seeders except private trackers and emulating it, and emulation isn't perfect. I'm not really sure what multiplayer Dolphin emulating is like and honestly I doubt it's any good. If you looked at it, the Wii list I posted earlier consists of almost just exclusives, and it's a pretty long list. And most games on the PS3 can be played on other platforms except for a very, very small number.
I'm assuming OP has a computer at home, probably one that can handle games at around low to medium settings (100% assuming on that). So why bother getting a console when you could just play said ports on your computer? Wouldn't it make more sense to get the console which has the games you can't play on a PC, assuming they're games you want to play in the first place? It would be cheaper or around the same price to get a Wii and upgrade the computer so it could play those multiplat games. But if OP wanted to play, say, Heavy Rain, Atelier and Flower then getting a PS3 would make the most sense.
Or, as I mentioned before, maybe get both and enjoy the best from both words. You can get second hand Wiis really cheap nowadays, I personally sold mine for about $70 without a problem and I doubt they're going to be much more than that. (Sold it because I no longer had a tv to play it on hahaha)
Also wow if you're getting bored after a few weeks maybe get some different games Don't say "it doesn't have any games which aren't shovelware", the link I posted earlier disproves that.