Think hard about buying a DSLR. I went with mirrorless after doing a ton of research, and also because of what I saw with almost every single one of my friends who bought into the DSLR "monopoly": they stopped using their cameras after a couple of months. Why? Because it's too big. The body is large, the lens are large. And heavy. Odds are, this will happen to you too.
As other posters will mention, the best camera is the camera you have with you.
Mirrorless cameras are a compromise. They are a compromise between image quality and size. For a lot of people, this is a worthwhile compromise over DSLRs. Honestly for most people, with the exception of pro photographers, MILCs and high end compacts (Canon S100, Panasonic LX5, Olympus XZ-1, etc) will do just as well as a DSLR. Most people will not be able to tell the difference in image quality between these cameras, especially photos taken in good light.
With most MILCs, you get enough shallow depth of field with the right fast prime lenses and you don't feel like you're carrying a brick with you. People are more relaxed around you, because they won't think twice about that "large" point-and-shoot you're carrying.
In my opinion Micro Four Thirds (Olympus + Panasonic) are the most viable MILCs now, due to the large number of high quality native lenses (disclaimer: I own an Olympus E-P3 and love it to death). Sony NEX series follows - they just need to release better/more lenses. Nikon's new 1 series (V1, J1) aren't of interest to me due to the small sensor size.
Go to DPReview.com and read, read, read.