If you are looking to go low cost, the Wii is good option, especially if you already have one. Lots of games, quick downloads, excellent emulation, pretty good image quality. Plus, easy to dabble in other retro consoles at any time without having to get a half dozen consoles hooked up with games for each. Break from Zelda LttP to play a level or two of Sonic and Knuckles? Awesome.
Wii does have some great adapters and SNES style controllers which work well with all retro games, but they all have a slight touch of lag from my experience. YMMV, and I'm pretty picky, so take that with a grain of salt.
Real-deal SNES consoles and carts will most likely last longer than your Wii and Nintendos non-existent digital download account service(might change soon?), but the hobby can become expensive.
Especially if you start collecting a lot of games in good condition and also invest into displays/scalers/etc to get the best quality experience. It's a deliciously fun downward spiral, and while it can be a burden on your wallet, it's completely worth it for the hundreds of hours of amazing 16bit games you can enjoy.