Well, I bet that you have played more then you think. For example, TF2 is a major game, and unless you bought Orange Box for no reason, you have played that. Probably a list of other major games as well, since I think most of us are guilty of imagining that games we enjoy are a bit more, "Underground" then they are, for the cheap indie cred.
Anyways, yes, if a major games seems to appeal to you, try it. However much one may whine that their disliked franchise of choice is overrated (And again, we all, or most, do this to some extent), very popular games got very popular for a reason. They are doing something right, and you might as well explore that. If you're actually looking for advice...well...very popular games tend to polarize people, so its hard to get down to the nitty gritty of pros and cons without descending into bickering. I can try though.
Play Portal if you like puzzles and puzzles solving, as well as black humor. The major problem with it is that it is too short, but since you own it anyways, its not like it would be an unwise investment.
Half Life Series is a real, "Gamers game". All the pieces fit together perfectly, level design, challenge, set pieces, pacing: its like a perfectly designed gourmet entree. Of course, if you just don't like the entree to begin with, it doesn't matter how well made it is. Half Life is a shooter with light puzzles, the story is solid enough but not exactly extensive, the weapons arn't over the top in power, yet it also isn't a terribly realistic, sim-ish shooter. If those are things you're looking for, maybe Half Life isn't your thing.
Bah, this would take to long, and I'm only really an expert on the Valve games on your list.