Alright I'd go with Nintendo Wii.
Here are some of the reasons
Virtual Console - over 200 games on the North American VC. Unlike Sony's PSOneClassics and Microsofts Arcade the Nintendo Wii has multiple platforms represented. Your essentially buying a TurboGrafix, MasterSystem, Genesis, 32x, NeoGeo , Commodore64. But your also getting a huge back catalog of Nintendo made titles from NES-N64. On the 360 you'll pay almost 20$ for a N64 game (Banjo) but on the Wii it'll only cost you ten bucks. Where classic Sega games cost more then 10$ on Live Arcade you'll get Genesis games for only 8 on the Wii. Now how about PSOneClassics, yes Sony has its own download store but it is limited to fifty or so PSOne games and yes they can cost as little as 6$ their isn't enough content to really keep you stuck to your TV Screen. I myself have spent over 200$ on my Virtual Console in my mind it is the best feature of the Wii.
Backwards compatability - Unlike the 360/PS3 the Wii has full backwards compatability with the Nintendo GameCube. Giving you hundreds more games to purchase. If you missed the GameCube then this is a major asset as their is tons of AAA+ quality titles on the GameCube. Go buy Windwaker, Mario:Sunshine, Pokemon Colleseum etc....etc....
Third party software - Yes the Wii is covered in cheap shovel ware with a side order of mediocre junk. But their are diamonds in the rough. Titles like The Conduit give you a Haloesk online experiance. Every day more and more third party titles are being released on the Wii. You have great titles from all major third party publishers and day after day more are joining up. Your own examples like Epic Mickey perfectly prove my point. Also games that come to the Wii are either fully exclusive or feature exclusive gameplay elements.
Online Network - Yes the online network lacks the finess of the 360 but it has plenty of positives. Take for example the everybody votes channel, the Opera channel the Nintendo Channel and all future channels. You can play your favorite Nintendo titles online against friends or people from around the world. The best part is the network is entirely free, unlike Microsoft's X-Box 360.
First Party software - You point out you aren't that interested in the Wii line of games. Well the great thing is your entering the generation years in. So you have an abundance of great first party games to choose from. SmashBros:Brawl, MarioGalaxy, MarioKart, LOZ:TP....etc....etc....
An experiance not found on any other platform - True motion controlls have yet to come to the 360/PS3. Sure the wand comes out in the spring but what software will utalize it? how many games next year are going to utalize the Wand. or how about Natal, which should cost about 200$ extra on top of the console. How many games will utalize Natal? You can get true motion controls right now with hundreds of titles utalizing them. Say you don't like motion controls you still have games like MarioKart, Brawl etc...etc.. that can be played with a GameCube controller or VC controller.
Price -At 209.99$ (CDN) or 199.99$ (US) the Wii is the best purchase for your money. of course I the long run I suggest owning all platforms but for now if you have to choose one then Wii is your best choice!