I'm very basic when it comes to yeast. I re-use yeast by salvaging it at bottling time from the FV, I use a sterilised spoon to put it into sterilised tupperware containers. It keeps well in the fridge - smell it when you open it. But only open it when you need to. Really good hygiene is needed around yeast.
I have mainly used dried yeasts to date. Sticking to English/American yeasts, as I generally do, some are very neutral, others provide a sweet fruitiness. I use both types. Safbrew S33 and Mauribrew 514 are sweet and fruity, I like them.
Nottingham/Gervin and S04 are less flavoured and slightly tart. I use Gervin in beers where I want the hops or the grains to do all the talking. I'm not a huge S-04 fan but many people are. I find it a bit sulphurous or something.
I have recently used Mauribrew Weiss yeast in a few beers, its not a real Weiss yeast, it's like a spicy ale yeast. Good in certain beers if you like a spiciness. I have a stout that it works really well in. The stout is very strongly flavoured, from the yeast and a lot of black malt.
S33 does not attenuate very well, it leaves an OG around 1018 in many beers, and I have combined it with Gervin to get the best of both worlds. Great flavour from the S33 and better attenuation from the Gervin, to reduce the sweetness to a level I prefer.
S05 is the standard American yeast, very neutral, which means you taste the hops and grains pretty much as they are. Which I also like. Like Gervin, but even more neutral.
I have used White Labs WLP002 liquid yeast a few times. I really like it and it is very popular with home brewers and microbreweries. It has a lovely flavour, a bit sweet, and it ferments quickly and clears really well. Micros like it partly cos it enables quick turnaround, their FVs are not tied up with one beer for long. But it also makes great beer. Wyeast 1968 is the same or extremely similar.