Here's my two cents: first off, there is no substitute for critical listening or auditioning equipment under controlled circumstances. That being said, seven years ago, a Sony CD player that was gifted to me died. So, I did my usual research & reading and went out to do some critical listening under controlled conditions. I listened to a Marantz CD6005, its direct NAD competitor in the same relative price point and an NAD player that was about $150 above the Marantz's price. I didn't have to listen very long to either NAD. I bought the Marantz. For my tastes, the NAD units were very flat in frequency response. So flat, that neither of them were nearly as musical and dynamic as the Marantz. I haven't heard the newer NAD players. So, I have no idea if this sound signature has changed. If you read reviews of players you will find that Marantz consistently outperforms almost everything in their respective price points, year after year.
My friend recently purchased a factory refurbished Marantz CD6006, largely because of how much he liked my CD6005. He is very happy with that decision. With the CD6005, I started with the conventional RCA analog hook-up and, then, switched to "AUDIO EX 2" mode. Very easy; done with the remote and a couple pushes of a button. This was a slight but immediately noticeable improvement in sonic performance. I now have it connected via Pangea digital coaxial cable, using it as a transport with the DAC in a McIntosh MA5200 integrated. I'm still trying to decide if this is an improvement over "AUDIO EX 2" mode. My immediate take is: maybe an extremely small increase or improvement in bass response but I need to listen more. Maybe the DAC in the MAC needs more burn in time because this is the first time I've used it. My friend has his CD6006 hooked up via digital coaxial to his Pioneer Elite AVR and he absolutely loves that player.
I'm not familiar with your amp. If it has a quality built-in DAC you may want to consider a transport, as opposed to a player. Here are 2 in your budget range that I've read good reviews of that you may want to consider: Cambridge Audio CXCv2 and the Audiolab CDT.
Good Luck!