Small footnote. Olympus actually doesn't embed all the same correction information that Panasonic does (some of the Leica lenses don't either). Panasonic lenses embed both distortion and C/A correction factors, but Olympus lenses only embed factors for distortion correction.
Andrew, there's
a stackexchange answer I posted a while back on some basic technique issues that a lot of newbs run up against and blame the camera for.
While that question was asked/answered for a Canon shooter, the same principles do apply in the case of MFT.
As for which lens to go for, if you want a fast normal prime in MFT, I'd actually say look at the Olympus m.Zuiko 25mm f/1.8. It came out
after the Panasonic Lumix 20/1.7 I own, otherwise I might have gone for it. It's more expensive than the Lumix 25/1.7, so if your budget doesn't allow or you want a pancake lens, then don't bother. But given that my favorite lens on mft is the m.Zuiko 45/1.8, and the 25/1.8
looks similar, optically, that would be my pick today. The main tradeoff over the Pana (aside from price) seems to be sharpness for vignetting (i.e., the Oly's sharper, but vignettes more wide open).
Just keep in mind, no lens is perfect. It's still made of glass, not magic air, and no lens has
an MFT chart that's a straight line across the top. Fast primes are good, sharp, fast little suckers at low cost, but they don't zoom, and nearly all of them exhibit LoCA (aka purple fringe) if used wide open in bright light.
However, as everyone else is counseling you, I'm not sure you know whether or not you really want a fast normal prime, yet.
Practice a bit more until you know what it is you need. Concentrate on whether you need a faster lens (more maximum aperture), a wider lens, a longer lens. Also, you can use Panasonic lenses, as long as they're for micro four-thirds. Just like Olympus, Panasonic also made "four thirds" dSLR lenses (i.e., you want a lens that's designated as
m.Zuiko,
Lumix G, or
Leica DG, otherwise it won't mount directly onto your camera).