@max_b , forget about brand wars. Currently Nikon is ahead in terms of dynamic range, but that can change any time. All brands have their pros and cons, it's up to you what you need, prefer etc. For instance Nikon struggles with consistent results and had quite a few faulty cameras in past years, but Nikon fanboys won't tell you that

Canon on the other hand is lacking in terms of evolution and they hide behind their marketing. Sony is quite limited when it comes to accessories and lenses, and it can be really expensive comparing to Canon or Nikon.
Canon 6D is a fine camera, I bought it just few weeks ago for myself and I'm really happy about it even though it's quite old (introduced 5 years ago). The problem with it in your case is that you're on a quite limiting budget. To buy a GOOD lens you need to reserve at least $400-500 for a single lens, even for used. By spending 2/3 of your budget just on a body you will need to settle with low performing lenses and you won't be able to use 6D to its fullest potential. Usually it's best to buy good lenses first, because they will stay with you much longer than a body. Once you have a nice collection, you can switch bodies pretty much every year if your financial situation allows it, because bodies are not that "durable". Lenses can last you over 10-20 years without a problem, but you will need to switch your bodies often compared to that.
So, ultimately it's up to your decision. Pick a brand and unless you have a VERY good reason to switch, stay with it. Switching brands after you've committed hundreds or thousands of dollars is not cheap nor easy. If you can, go to a store and try these cameras personally. You will know which you prefer more, which grip is better for your hands etc. Also some stores offer camera renting (let's say for few days or even few weeks), so maybe that would help you too to make the best decision for you.
Once again, I can't stress this enough, don't listen to people advocating "brand xyz is better!" or "dslr/mirrorless is much better!!!", because that's never just black and white. Don't forget that your gear are just tools. Pretty much any camera can give you great results if you learn how to use it.