Not only am I not an expert, I'm repeatedly reminded how little I know about music theory! Thanks for that, and if I can pick your brains a bit more (or anyone reading)... I'm puzzled. So, you say that in 6/8 time there are two beats, so it's counted something like 1 & & 2 & &, where I - probably mistakenly - thought the 6 meant there are 6 beats, and the 8 meant they are eighth-note beats. Am I conflating the time signature note number with beats?
So how do I know how many "beats" there are in a time signature - is there an accepted method? If I take six divisions and count them 1 & 2 & 3 &, I can make up a tune just fine. I imagine, however, that it would normally simply be notated as 3/4, but it would be clear that it's a compound time where each of those beats is - or can be - a pair of eighths.
I also have a vague memory of learning that the choice of note value in the time signature is to do with a range of tempo traditionally allocated to the notes, but that's maybe a separate issue.