Choose the amp you like the sound of best, and then add the matching player, as the differences in amps are much bigger than the differences in CD players. And if you'd just said rock, I'd have said Exposure, but seeing as you've added jazz and soul, I'll say Cambridge.
I'd also veer towards the Cambridge player anyway since it has a digital in so you can take advantage of its DAC for lossless streaming.
I'd listen to Rega as well, they're great fun. Marantz mid-range (ie PM7001 etc). If you're buying new, Primare is pushing it a bit, but there are some excellent s/h deals around for the older models like the A30.1. You might also be able to pick up the old-model Roksan Kandy pair really cheaply now that they've been replaced. Lastly, don't discount the Rotel RA-06.