Connect dac to Music Hall CD-25 or upgrade?

Current system:
CD Player: Music Hall CD-25
Integrated Amplifier: Musical Fidelity A300 Integrated
Speakers: Joseph Audio RM25si Mk II's
Speaker Cable: Analysis Plus Oval 12 speaker cable
Interconnect: Alpha Core Micro Purl I/C
Still using stock power cords

Here's the question:
I want to upgrade the Music Hall. I have about $1500 to spend. Am I better off using the Music Hall as a transport and spending all the $ on a DAC or should I sell the Music Hall and buy a whole new CD player? I listen to a lot of small jazz combos, female vocalists, some chamber music, and, lastly, some good old Grateful Dead.

Thanks for the help.