I think that most would agree that the DAC has a more significant impact on sound quality than does a transport, especially at your price point.
Test 1: Connect your CD player in parallel through the DAC and directly to the system for an A/B comparison of sound quality.
Test 2: Connect a 2nd CD player to the DAC using an identical CD and do the same A/B comparison.
I suspect that you'll confirm that the DAC is a better upgrade.
Also, a DAC can be used with multiple pieces of equipment. I do not believe that you could get a new CD player that can double as a DAC for your budget.
Test 1: Connect your CD player in parallel through the DAC and directly to the system for an A/B comparison of sound quality.
Test 2: Connect a 2nd CD player to the DAC using an identical CD and do the same A/B comparison.
I suspect that you'll confirm that the DAC is a better upgrade.
Also, a DAC can be used with multiple pieces of equipment. I do not believe that you could get a new CD player that can double as a DAC for your budget.