For your budget, you're going to have buy used if you want a DSLR. Since the principal advantage of a DSLR over a P&S for a semi-skilled user is DOF control. So to accentuate that try to shoot with a "prime" lens (one with no zoom) these tend to have a smaller "f-number" which indicates that you can open the aperture wider resulting in a shallower DOF and better low light handling.
I'd suggest you prowl amazon KEH and ebay for bargains. I prefer Amazon due to the ease of returns.
They have a Nikon d5100 (mid-range model from a few years ago) with a kit lens for around 300. This will do better in low light than same age Canon's.
https/www.amazon.com/gp/offer-listing/B004V4IWKG/ref=olp_twister_child?ie=UTF8&mv_customer_package_type=0&mv_style_name=1&qid=1488597390&sr=8-1
There is no significant advantage to one brand or type.
Older Nikon's and Pentax's do better in low light compared to their peers because of their sensor performance (check dxomark.com to compare).
Canon and Nikon have the most lenses to choose from. This won't matter for a while, but will if you stick to it.
These older Nikon, Canon and Pentax cameras auto-focus in video slow. If you shoot manually, you won't care.
Mirrorless cameras (Olympus, Panasonic, and Sony) auto-focus in video much faster. I prefer Panasonic from this group.
Check prices yourself. Give yourself some time to learn to use the DSLR; the skill to control the light, aperture, shutterspeed and ISO isn't going to happen overnight.
A tip on shutter speed: Keep it at roughtly at the inverse the of twice the frame rate. So if you are shooting at 30fps, set the shutter speed to 1/60. I've seen alot of crappy beginner videos where they apply photography logic to video and set the shutter speed high to avoid motion blur (which is actually desirable in a video).
To add a prime lens you had better start saving. Use the kit lens to start off with. The kit lens will teach you what focal lengths you like to shoot at. So if you end up at the wide end a lot, look for a used 20mm f/1.8 lens.... in the middle? a used 35mm f/1.8 is cheap. At the long end? A 50mm is also cheap. The 20mm will be between 300 and 500. The 35 and 50 can be found for as little as 100 with a little luck. If you need something longer a used 85mm f/1.8 typically runs 2-400.