I would say the best thing you can do is go shoot a few of them that are in your budget. Most places with a pro shop, such as sportsmans warehouse, North40, etc., are more than happy to set up a few bows so you can shoot them if they have a short indoor range. A single cam is a good suggestion by Marty, they simply do not go out of time on you. I have a Bowtech with a binary cam system that is supposed to "slave" them together so they don't go out of time, but I have had it do just that once already as the string got more and more shots on it. Not a lot...but enough to affect my groups so that I noticed something wasn't right. I'm fine with that as I like the extra speed the cam system gives me, but others may not.
Most new bows are pretty dependable these days, there really isn't one I'd be worried about buying if I liked it...barring a Chinese knock off or something like that of course. Some will have decent accessories that come with them and some won't.
Take a day and go shoot some different ones. Then you'll know what feels good to you, which ones are quieter, which ones have cheap accessories that rattle during the shot, smooth draw cycle, good back wall, good hunting type rest, fiber optic pins that aren't too big or too small, etc.
Amazon can be a great resource for reading reviews on items even if you don't plan to buy from them.
If you are going to shoot it instinctively with fingers, then disregard the next info, but once you choose one I highly recommend a d-loop and a peep size that matches the outside diameter of the sight. I always choose a round style sight frame and then like the peep size to match to the sight frame so that I can align the sight frame with the outside edge of the peep. It is like using a peep sight on a rifle that way, your eye will automatically center it and it's yet another reference point for you to align when shooting. As an archer you know that it is a game of doing everything the same way every time and hitting your anchor/reference points.