A mirrorless is a system camera and you must therefore carefully consider the system. There 2 major differenciators between systems:

• Sensor-size: This affects image quality and particularly low-light performance. Four-Thirds and APS-C are popular sizes but there are full-frame options and smaller 1" or 1/1.7" ones too which have noticeably lower image-quality than larger ones.
• Lens Mount: The family of native lens available for most mirrorless mounts is relatively limited when you compare them to DSLR lenses. Micro Four-Thirds which is the first mirrorless system has quite a few lenses and so does the Sony E-mount system (For APS-C mostly) but lenses in Fuji, Canon EF-M and Nikon 1 mount exist in much fewer numbers. Third party manufacturers do fill some gap but follow market popularity. So you will see much fewer third-party lenses for XF-mount and EF-M than for E-mount or Micro Four-Thirds.

While mirrorless cameras enjoy a wide number of adapters to use lenses for other mounts, most of them come with some serious limitations. Sony, Canon and Olympus/Panasonic have preferential compatibility with their own DSLR lenses, meaing that you can use an A-mount lens on an E-mount camera or an EF-S one on a EF-M camera with better integration.

Weight is a huge motivation factor for getting a mirrorless system. Of course, the larger sensor and correspondingly larger lenses needed for better quality have to be balanced out with the desire for a lighter system. Still, if you look at the specifics, the relation is not entirely proportional. There is less difference between equivalent MFT or E lenses than one would expect.

Then you should consider camera specific features. Most mirrorless cameras do offer full manual controls, custom WB, bracketing, metering, etc but coverage of advanced features differs:

• Image stabiliation can be provided in-camera or in-lens but not all lenses are stabilized. Legacy lenses or those used via an adapter benefit more from being paired with in-body stabilization,
• Weather-sealing is only available in some models. This is extremely useful for shooting in rain or snow. It must be combined with a weather-proof lense which are in very limited in some lineups. So if you are interested in photography in adverse weather, make sure your chosen system has the body and lenses you need with weather-sealing. Only one mirrirless camera exists which is submersible without a special casing, that is the Nikon 1 AW1 which I reviewed here. This unique option takes a lot of compromises, so read about it, if that interests you.
• An EVF is essential. Some cameras support an optional external one which usually blocks the hot-shoe. Built-in EVFs are very good now with resolutions up to 2.8 MP and fast refresh rates. In all cases, they give much better visibility than the rear LCD. Plus, they add stability when shooting hand-held.

Look for particular features which interest you and pay attention to details. Long exposures of 30s are supported by pretty much all but if you want to do longer ones, then you have to read the specification carefully. Some have Bulb modes which stop after 2m while others last an hour which gives you nice star trails. You can approximate this by exposure stacking but it requires more work. A special nod is deserved here to Olympus which implements Live-Bulb so that one can see an exposure form during BULB. No one else has this and is extremely useful for things like fireworks where it is difficult to predict the time needed.