DSLR or Mirrorless Advice (which models)

[petrochemist118 143]

DSLRs are better for action shots, but for low light work mirrorless cameras have big advantages.
As far as lenses go, as has been said before mirrorless cameras can use adapted SLR lenses, and other legacy lenses such as enlarger lenses. They will (nearly always) loose automatic features when adapting lenses but there are a few more expensive adapters that can still use more advanced features from a lens.
Some lens/camera combinations allow the adapter to contain a focal reducer (basically a teleconverter in reverse) that increases the FOV & brightness on the sensor. This can be useful in low light shots!
Larger/newer sensors will be significantly better in low light w.r.t. noise, but recent full frame models will be out of your price range (The Sony A7 is apparently great in low light)

All my cameras were made before 2013 so things have improved, however both the Panasonic G5 (micro 4/3 mirrorless) & the Pentax K5II (APS-C dSLR) work quite well in low light conditions and were under $300 when I got them.

Unlike Gary I've tried multiple cameras & know ergonomics make a huge difference to how usable a camera is. You should be able to get reasonable results from any modern camera but one where the design suits you is much more enjoyable to use!