They are all good for stills as well as video; the 60mm is the star and I use it more than my 75mm. In the US, they have four year warranties. If you don't want all three, at least get the 60mm. I suspect that with that lens, you could probably save the money you would spend on the Oly 75mm. And, you might also not have to buy the 45mm - good, portable lens, but for many people the Sigma can take care of the 45-75 needs.
I agree with another poster who recommended the Pany 14mm; I use it a lot - also good for stills and video. However, I don't agree about the Pany 20mm recommendation. It has a good reputation because it was the only decent prime for m4/3 years ago, but now we've moved on. It's an old design that focuses slowly, and (both old and new versions) are over-priced. I sold mine almost two years ago; it had come with a GF1, which I kept a lot longer than the lenses I bought with it. It is very portable, though, so if you find a cheap one, it might be considered instead of the Sigma 19mm.
Note: I have all of the lenses discussed above and they are used on GH2/3 and EM-5 bodies. I also have the 9-18, 45-175, and 100-300 zooms, all of which I like. I shoot stills and video equally, although I prefer a DP2M for stills.