Grab a used Nikon D7000/Canon body for $400. You might be able to get one even cheaper. You can buy a Tokina 100mm new for $400. This Tokina is the best bang for your buck of any of the ~100mm macro lenses on the market right now. You can probably grab a kit lens for general use as well for about $100 if you wanted. Alternatively you could get something the like the Nikon 60mm 2.8D for $225. It's also fantastic, but needs to be closer to your subject than the 100mm.
If you shoot under T5/Halides, I don't think blue saturates will be an issue. With LEDs its best to shoot in the cameras RAW format and edit it in Lightroom.3
Windows 10 now has the ability to natively edit RAW files if case you didn't want to buy software. It will change the color temperature to a more neutral tone. There's some free software out there for editing raw camera files as well.
It's more about the lenses than the camera itself. So any body will do the trick, but find the lens that will suite your needs. Mirrorless is good, but you get more bang for your buck with a DSLR. The DSLR system is more developed.