There's so many factors that go in to choosing the correct camera setup, it's always tough to give a good recommendation without you having a very specific use case and without knowing how dedicated you are going to be to photography in the future.
Nikon, Canon, and Sony are the 3 most common brands. All would be good choices. You just need physically hold them and go through the menus and see which you like best. I shoot canon but I feel like Nikon is a little better bang for your buck, money wise. The lens is the most important part of the camera. For wildlife (birds especially) you want a pretty long focal length. I would say 300mm minimum (on a crop body camera). 400 or longer is more ideal. Good lenses can cost even more than the camera and typically weigh a ton (compared to kit lenses). So you have to balance size/weight vs portability.
Mirrorless is the future but there's nothing wrong with using a DSLR. I think it's better to learn one if you really want to master photography as a hobby. I also recommend buying used gear. You can get a lot more for your money this way. Plus if you decide you don't like the gear or you want to upgrade you can sell the gear without taking a huge hit. More than half of my gear I bought used.
All I can speak to is Canon because it is all I have used. Your $1500 budget kind of puts you in an odd spot for Canon gear as far as wildlife photography is concerned. $1500 can get you a very good mirrorless camera (R7) but won't leave anything left for lenses. For $5-600 more, you can get an R7 and an RF100-400 lens (which is a "decent" but a little slow, wildlife lens). Now I definitely do NOT recommend spending $2k+ just to figure out if you like wildlife photography or not. You can do that for much cheaper.
So really, I would look at getting a used Canon 80D (DSLR) for $500 or maybe a 90D if you can find one for around $800 or less (much more than this and you should start looking for used Mirrorless R7 instead) then buying either a 1) Canon EF-S 55-250 IS STM ($150 "kit" lens, cheapest option to feel out wildlife photography on a budget), 2) Sigma 100-400 ($700) more of a dedicated wildlife lens but still budget friendly.
If you want a little more of a higher quality, dedicated wildlife lens you could opt for a 3) Canon EF 100-400 IS II ($1300 semi bulky/heavy but a very high quality lens for wildlife), or 4) Sigma 150-600 ($900 big/heavy but a decent lens). You definitely need to hold these lenses in person to get a feel for the size/weight before buying, they are big and heavy. (If going Nikon, a used 200-500mm would be a very nice wildlife lens and can be had for ~$800, which leaves you plenty of money for a nice camera).
You will also need a more wide angle lens for general purpose use and landscapes. Most 18-55 kit lenses will get you started for this on the cheap. The Canon EF 50mm F1.8 STM is also a great lens for portraits and macro, it is less than $100 too.
Hopefully someone else will chime in. Do consider I am coming from a primary wildlife shooters perspective. There are definitely better lens choices for nature, landscape, and general use, than the larger wildlife lenses I listed. And again, I would not hesitate to buy Nikon or Sony either.