As I understand it, the selection of malt (and adjunct), hops and yeast all affect the flavour of a beer in important ways. However, while you can taste the malt and other grains to get a feel for what flavour they will give to the beer, and you can smell hops to get a feel for flavour and aroma (and use alpha acid level as an indicator for the bittering hops), I can't see a good way to get an intuitive feel for the effect of different yeasts.
If there were only two or three yeasts, this would be fine: I could just try them all on some kind of reference mash. However, there seem to be hundreds.
So: firstly, other than the obvious (like top fermenting vs bottom fermenting), is there a standard way of categorising yeasts? I'm mainly interested in ale yeast at the moment, but broadly curious about the whole range of yeasts.
Secondly, is there a good way to get an intuitive feel for which yeast to choose for a particular job? At the moment I feel as though my technique is "pick the yeast whose name sounds closest to the beer I'm trying to make", which is obviously pretty terrible. Any and all advice gratefully received.