I'm not sure how advanced a photographer you are, but keep in mind that you'll get better results with a cheaper camera and a nice lens than a more expensive camera and a kit lens.
This is pretty much it.
In a nutshell, shop for the exact lens you want first, then buy a camera body which happens to fits it. If you don't know which focal length of lens might be best for you (and I'm assuming you used some sort of zoom lens on your current/old camera), you can browse through the metadata of your photos and see what focal length you tend to use the most - that's a good starting point.
I would also suggest a lens with around f/2.8 aperture. Lower (larger opening) can be great, but unless you're taking landscape shots with it (i.e. focused on infinity), anything inside with people for example, the depth of field will be super shallow (like a person's face can be in focus, but their nose, ~1" closer to the camera can be out of focus...so a f/1.2 or 1.8 lens has limited uses in some ways).
Anyway, I just went through picking a new mirrorless camera two weeks ago. My previous kit was a Sony A6000 with 16-70mm f4 lens, and a 12mm Zeiss for landscapes. Use a fancy Canon 5D? at work – but that thing is a beast in size/weight. I went with the Sony A6400 and the new Sony 16-55mm (24-70mm full-frame equivalent) f/2.8 lens. This will put you well over your budget unfortunately (the kit lens really isn't bad fyi).
It was between a Sony and a Fuji this time around, and I was even looking at used full-frame cameras too (sadly just for the lens it was still like $1500 alone for one of those). Then I found a website and made the below comparison photo. It really came down to how I didn't want a huge/heavy camera for travel, but STILL still have a camera with a decent wide to medium-zoom lens at f/2.8. That lens for most professionals (and enthusiasts) has always been the 24-70 f/2.8. You can see the pretty massive size difference here - each has an equivalent 24-70 f/2.8 lens (and even the Fuji is a decent amount larger):
