I've always liked They Might Be Giants but I've only got 1 album (mink car) which isn't their best, and a few songs on compilations. I'm thinking of fattening my collection, but what is their best album?
After many years of thought on this subject, I've come to the conclusion that "Lincoln" is their best album. It's got just the right combination of musical inexperience and experience (being their 2nd album) -- showing their musical greenness and yet giving them a bit of a critical, rough edge. Also, it's got great songs, great lyrics, and of course, my favorite album name and artwork as well (actually, Flood's name and artwork are nearly about equal on my scale).
Still, "Apollo 18" is usually my personal favorite because of nostalgia reasons. Its songs aren't particularly strong standing alone, but they come together quite nicely to make a good
album.
Many people consider "Flood" to be their best album -- and it really is a great album, but hard-core TMBG fans shy away from it because "everybody else" seems to like it. It has been their most commecially successful. I'd say it's their second best album. Although..
Oh well, I'll just make a list. As you can see, there are five levels of TMBG greatness, and some albums are tied with others on the same level:
1. Lincoln
2. Flood, John Henry
3. Apollo 18, They Might Be Giants
4. Mink Car, Factory Showroom
5. No!
I've not included compilations like "Miscellaneous T," "Then: The Early Years," "Severe Tire Damage," etc.
John Henry is completely awesome, but it is essentially its own beast that stands out from the rest of their work in my mind. It's consistency in style and musical quality is stunning, but it may take you a while to get used to it if you were weaned on earlier TMBG stuff.
So, my advice: go buy Flood and Lincoln next.
Hope that helps.

Benj