@rudyb In that price range I bet most players will have a good DAC built in.
This is quite right - however what is at issue is the transport. For this you really need something dedicated, and that is the tricky bit. This is the next logical step up the ladder. Perhaps a few steps up.
With transports it is a 100% technical thing. Which one reads the data on the disc the best, and whatever accompanies that rather functional task. Traditional CD players have many other functions to perform, of course, and design compromises are made that are not an issue with a transport.
The OP was not asking about streamers.