To start, taking DSO images requires 3 things, only 2 of which are mentioned in your post: Mount, telescope, camera.
Since you didn't make any mention of a camera, I will start there. If you already own a camera, great - that will make this easier.
If you already own a DSLR camera, that can be used for DSO imaging. You would only need a mount at that point. If that is the case, and you don't plan on travelling away from home to image (and maybe even if you do) - I would skip the tracker mount since it is only motorized on 1 axis, and get an EQ mount instead. There are mounts you can get for $1,000 that can handle small scopes or a DSLR+lens with no issues. Notice how I went right to spending your entire budget on a mount? That would be the best possible scenario here, because the mount is by far the most important part. Until you save more for a telescope, you could just mount your DSLR+lens, which would work just fine (a lens is basically a telescope with a helical focuser, and sometimes, autofocus bits). Start with the shortest focal length you have, and work your way up. Shorter focal lengths are always easier, at every step from image capture to processing. This is probably the most important thing to learn about DSO AP - keeping focal length short helps you learn faster, and create better images. Increasing focal length increases difficulty at an exponential rate.
If you do not already own a DSLR camera, well you're going to need one of those too. I am not the person to make recommendations, as I have never owned one, but I have considered it in the past, so I have done some research. It seems a lot of folks who use a DSLR for AP use either a Canon or Nikon as they are the most astro-friendly, and it seems that more folks use the Canon 6D than any other model of DSLR. The downside if you don't have a camera already is there goes half your budget, which means the star tracker is your only option to stay within the $1,000 budget. Either way, you'll have the tools to take pictures, but EQ mounts are easier to live with than star trackers. Star trackers are much lighter though, so if you plan to leave home for darker skies every time you image, then the star tracker might be the better choice. But I can't think of anyone who would rather use a star tracker at home than a standard EQ mount that is motorized on both axes.
Good luck with whatever you decide, and make sure you do your research before buying anything.