From a practical standpoint, while there were only a few games made for the system that I ended up being interested in, the Nintendo Wii is probably the one I like the most. There is and was a lot to love about the system. The Shop channel giving you access to a bunch of retro games for various different systems via the Virtual Console was awesome. One of my favorite games, Fire Emblem: Radiant Dawn, was on the system. Back in the Wii's heyday, when they were actually operational, I found the News and Weather channels very nice to use. Wii Sports was a fun tie-in launch title game. Most important, however, is that it is backward compatible with the GameCube, complete with the ability to insert GameCube controllers and GameCube memory cards into their respective slots. It wasn't the most graphically impressive console and there weren't that many third party titles that you'd want to play online with friends, but I've never been someone who cared about games (or movies, or anything really) having the best graphics and had an Xbox 360 at the time to play games with friends. There are/were just a ton of positive aspects to the console, and I still play games on it from time to time.
On a fun level, there are numerous contenders.
The Sega Genesis was the first video game console I ever played and there were a ton of fun games to play on it.
I have a lot of fond memories of playing games with friends locally on the Nintendo GameCube and it has a great library of games, including but not limited to my favorite game of all time Fire Emblem: Path of Radiance, Kirby's Air Ride, Luigi's Mansion, Super Smash Bros. Melee, and Super Mario Sunshine. It's a really solid console with a great controller.
Likewise, I have a lot of fond memories of playing games online with friends on the Xbox 360 back when it was current. It is also useful in that it can read DVDs, stream Netflix and Twitch, and give you access to YouTube, among other various apps.
I also have to mention the Nintendo DS and Nintendo 3DS, but particularly the Nintendo 3DS. The Nintendo DS had a number of very good games and the Nintendo DS Lite even allows you to play Game Boy Advance cartridges and has an alarm feature that I've used a number of times in the past. The Nintendo 3DS, meanwhile, is probably up there in contention if not the console I've spent the most time playing games on, at least in the past few years. The 3DS gave me the opportunity, for the first time, to trade Pok?mon and battle other trainers from around the world despite being a Pok?mon fan since 1996 when the series first came to the US. That was back in the Pok?mon Black and White days, and I've been using the online functionality in all the main series Pok?mon titles ever since then. Then there's, of course, Animal Crossing: New Leaf which I've spent a ton of time on over the years. Fire Emblem Echoes: Shadows of Valentia, the 3DS remakes of the Shin Megami Tensei: Devil Survivor games, DS backward compatibility, a rudimentary YouTube app, free online service, and the wide selection of new and retro games found on the Virtual Console are also awesome.