There are many camera models in the mirrorless market but I think the decision of which camera to get is pretty easy. Here is my simplified view of it.
If you are a beginner and you just want to shoot photographs in automatic everything mode, The Sony NEX line, in particular the Sony NEX-F3 is what you should get. If you find an old clearance model NEX-5N, I would also consider it. I have the first model NEX-5 (read about Sony NEX my experience) but today, I would suggest the entry-level NEX-F3. You get a good sensor that is not too different from NEX-5N and the even more expensive NEX-6. The body is more plastic but everything you need is there. I would skip the WiFi and Apps feature of the NEX-5R. The Sony NEX user interface is not their strength and adding apps to the mix just increases complexity.
If you are a more serious photographer that would like to twiddle the dials and learn more about the camera, I would buy a Olympus Pen camera, either the E-PL5 or the E-PM2. If you want more features, controls and a built-in electronic View Finder (EVF) then get the OM-D E-M5. I recently bought the E-PM2 because I value a smaller size over additional features. All 3 cameras have the same picture quality, sharing the same 16MP sensor and image processor. The Olympus is my favorite and I now own 4 cameras, 2 E-PL1s, 1 E-P3 and E-PM2 (read about my Olympus Pen experience).
Why do I steer the beginner to the Sony and the advanced user to the Olympus? I think a beginner can make better quality photographs with the Sony NEX, set simply in automatic mode. The Sony has a bigger sensor and better low-light capability. Its Intelligent Auto mode does a great job thinking for the beginner. The movie mode is also better than the Olympus and makes better home movies. The Sony lacks a good lens selection, but for a beginner, this won’t matter as much. For the enthusiast, however, the available lenses for Olympus are unmatched, they share the micro 4/3 format with Panasonic. For people who like to shoot with prime (non-zooming) lenses like me, the selection of high quality glass is fantastic. I believe a knowledgeable photographer can take a better quality photograph with a Olympus compared to the Sony.
Panasonic, along with Olympus are part of the micro 4/3 standard and share the same lenses. I prefer the Olympus over the Panasonic for two reasons.
1. The Olympus has in-body image stabilization which works with any lens. Panasonic does not. In fact, since I use big aperture Panasonic primes lenses on the Olympus with the image stabilization, I can lower the ISO and get higher quality photographs.
2. This maybe a personal preference but like the Olympus color and exposure better. I find the Panasonic to be darker and with duller colors.
The Panasonic, however, has one large advantage over the Olympus, in videos, especially the GH series. In fact, professional movie makers use the GH2 and some say it rivals the Canon DSLR in video quality.
Mirrorless cameras are great for general purpose photography but they are not ideal for sports. This is where the traditional DSLR has the advantage. There is one exception. The Nikon 1, is a mirrorless system that has high performance that rivals mid-level DSLRs for action and sports. However, its image quality is not as good as the Sony or Olympus. If speed is the primary factor and you don’t want a DSLR, consider the Nikon J1 or Nikon V1. Both are available at significant discounts since Nikon initially overpriced them and they didn’t sell well. If sports shooting is not important, stick with the Olympus or Sony.
Fujifilm has a passionate following for their retro styled mirrorless X-Pro 1 and X-E1. They are expensive, slow focusing, weak in video and their special sensor does not work well with mainstream RAW conversion software. Canon was the last major manufacturer to the mirrorless market and their EOS M is a disappointment. It is not worth consideration at this point.