Jitter is a significant reason why various transports may sound different with the same DAC. Some newer DACs feature reclocking which virtually eliminates jitter in the digital stream. Jitter can also be reduced by careful impedance matching between the transport, cable, and DAC.
With that being said, CEC belt-drive transports have been lauded for their ability to reduce mechanical vibrations and their jitter-inducing impacts. The TL51X would be in your price range.
Personally, I have a Bryston BP25DA which does have a reclocking DAC. So, I plan to purchase a new, inexpensive CD player to use as a transport. I'm looking for good ergonomics and reliability above having the lowest jitter output. I'm looking at several sub $500 units would work well for me.