Haven't played ThatGameCompany's stuff so I can't really give an opinion one way or the other. At the very least you're probably in for a pretty unique and/or original experience if you go with them though.

Of the other two, I have to recommend Uncharted though. It's a fun series pure and simple if you like that Indiana Jones pulp style. The gameplay is also solid. A bit less refined in the first one, but pretty much perfected by the second. And the writing, while obviously not serious all of the time, is solid the whole way through, and gets surprisingly mature in the best possible way by the third as far as the characters are concerned. Actually, the third finally sold me on Drake as a legitimately interesting character, and his relationship with Elena is probably the most believable video game romance I can think of at the moment.

As for Mass Effect, I've been pretty up front about my general dislike for Bioware even during their supposed heyday. I don't care for their writing, and I found the original Mass Effect to be both annoyingly predictable with it's main plot, and hopelessly boring with just about all of the side mission stuff. And if you try to look beyond that stuff with the first game, all you're really left with is a mediocre third person shooter. Now, from what I've played of the later two games, it seems it became a better third person shooter, but I still wasn't impressed with the writing. And the whole ME3 ending fiasco didn't do much to bolster my faith in their ability to write considering even a lot of fans were pissed off by that one. I basically dropped the series after ME1 and have no real regrets. If you want a well written RPG, I think there are better series out there, and if you want a good third person shooter you should be playing Uncharted anyway. A lot of people will disagree with me I'm sure, but I don't think you're missing much if you skip Mass Effect except a lot of mediocre writing and some wasted time.