I bought a Brother PE770 on Amazon for around $550 a couple years ago. I just checked and right now it's listed for just under $600. So it's a little over your budget, but it's a nice machine. I was hesitant to buy a machine online but it arrived in perfect condition, with perfect tension. I haven't had to adjust a single thing. I haven't used it a LOT and am still learning all the ins & outs of stabilizer, etc. but so far all the problems have been due to me and/or the products I was using and not the machine itself. The reviews on Amazon are mostly positive as well.
It's not super fancy but I didn't need super fancy. It comes with a 5x7 hoop and can also do continuous designs in a larger 12x5 hoop (which I bought but haven't tried yet). You can also buy extra hoops for smaller projects and there's a hoop specifically for embroidering baseball caps too. It comes with a few designs; I buy mine online and keep them on a little USB thumb drive that plugs right into the machine. Works great, very easy to use. I do wish the screen was a little bigger and better, but it's useable and I wasn't willing to pay the extra it'd take to get a better screen.