I would stay away from the Emotiva player. I would go with Marantz or Yamaha if a CD player is what you want.
The Audiolab and Cambridge transports are not CD players. They require a DAC. I believe this to be a good way to go, transport and DAC, just want to make sure you understand this. It can be done within your budget. More money will be spent on the transport. A budget DAC from Schiit Audio would likely be as good as those in players within budget. An inexpensive DAC could be replaced at a later date if you desired.