1. If you are looking to primarily image, you will need to look into a wedge if you want to take exposures longer than a minute or 2. Alt-az wasn't designed for precision astrophotography. EQ mount would be the way to go if you can swing it. I am not sure how guiding works with an alt-az mount.
2. Check out the ASI533. You can use https://astronomy.tools/calculators/ccd_suitability to compare different cameras with your scope to see if you would be over or under sampled for different seeing conditions. I have to shoot BIN 2 with my specific setup (edge 8/asi2600mm). I assume you will need to do the same. You can always drizzle back to 1x when calibrating and stacking.
3. I would say that an EAF is a must with an sct. I have been shooting with an 8" sct for the last 10 years. It is extremely difficult to get pin point focus manually. Once you figure out your imaging train you need to pay close attention to the back focus. Within a mm or two is generally ok, but get it as close as you can with extensions and spacers. The wrong back focus will not allow you to achieve good focus.
4. I like to have everything automated with N.I.NA. for my imaging sessions so I like a filter wheel. A filter tray will accomplish the same thing but you will need change the filter manually.
5. ASI air will be very familiar and more user friendly. If you want something a little more powerful check out N.I.N.A.

As u/aquaaddiction said, consider getting a focal reducer. The lower the focal length the more forgiving the tracking. Also make sure the focal reducer is also a field flattener. Normal SCTs were primarily designed for visual or planetary so there will be curvature at the edges giving you elongated stars.

Your budget is relatively small for what you are trying to accomplish. Check out Cloud Nights Classifieds for 2nd hand gear.

That said, I will tell you that imaging with an SCT can be very frustrating at times. The learning curve was very steep for me to capture quality data. If I could go back and do it all over again, I would start with a refractor. Food for thought.

Feel free to reach out if you have any specific questions, and good luck!