At the price range you listed, you have a lot of options. In the hobby arena, you would do better with the X-Carve pro, it comes in 4 x 4 and 4 x 2 sizes, but you can feed 4x8 sheets into it, the software allows you to run your program, then move the sheet, then continue the program, so you can machine sheets with some manual placement between runs.
I have no relationship with them, I personally use an openbuilds lead 1010 (they now have a 1515, 1.5m x 1.5m), for under $2k, but you need to build the machine from the parts they send you.
Accuracy is fine for woodworking, but for any type of metal work, or high precision work, things can get a little iffy.
The issue I have with all the hobbyist CNC machines, is that they tend to use all in one driver boards with small servos/steppers. Any CAD/CAM software that speaks GRBL will work fine, but if you want to step it up a level and use LinuxCNC, you will need a controller board that differs from what most of the hobby machines use. Look into the MESA boards.
Another option, is excess or liquidation auctions. Unfortunately during the current economic climate and the pandemic, there are many shops and factories closing down, and the equipment is auctioned off. You can pick industrial grade equipment for dirt cheap.