You're not being thick. Thirds can be either major or minor, as you've pointed out. And since the song contains both major thirds (C and E, F and A) as well as minor ones (E and G, D and F), I simply lumped them all together under the category of "thirds."
As to what's "appropriate," well, that's a matter of the song in question. If the chords of a song are diatonic, that is they involve only notes from the key a song is in (so in the key of C, we're talking about C, D, E, F, G, A and B), then you'll run into very specific patterns. Using the key of C again as an example, the thirds based on the root, fourth and fifth positions will be major (C and E, F and A, G and B) while the thirds based on the other scale degrees will be minor (D and F, E and G, A and C, B and D).
But if a song borrows chords from outside of a key, say a D chord pops up in the middle of a song in the key of C (and D has an F# in it, which is not in the key of C), and if you wanted to play an inverted third to go along with that chord, then you'd have two choices: D and F#, which is major, and F# and A, which is minor. So it really depends on the chord progression of a song.
Getting along with thirds is pretty vital to guitarists, because the standard tuning of the guitar make playing thirds and inverted thirds very easy. Not to mention they sound so good. You might want to take a look at the lesson called The Power of Three for a good breakdown on how thirds are used to build chords.
Sorry for the confusion and I hope this helps.
Thanks David. It does help a lot. Unfortunately I'm the kind of guy who has to have these nuances explained; which you do very comprehensively and in language that I can understand!
I need to do lots more reading on thirds, so thanks for the pointer to the article. It was suggested in the lesson, but who does what they're told the first time? :D