I recommend a 12” stabilizer with a 8” backbar this has helped my bow a lot, it takes some playing around with the weights until it holds the way you like.
Buying used bows is the best way to get a bow that performs great on a budget. With around $1,000 you can find high end fully set up bows from a few years ago that will perform better than a brand new bow that will cost the same after you get it set up.
You definitely should go into a shop and shoot as many bows as you can. Picking a bow is a lot about personal preference. Definitely save some of your budget for a really nice sight, rest, and arrows all of that stuff can run surprisingly expensive.