About six months ago, I caught the audio bug from a friend and neighbour, at which point I decided to upgrade a few components. However, I'm on a budget and so my kit is fairly modest. The NAD integrated amp and tuner, the Kef Q5's and the Monster power bar, purchased last Fall, brought my system to what I feel is introductory-level hi-fi. In January, I added the van den Hul interconnects, which were a noticeable improvement.
The CD player is currently the weak link IMO. I've been thinking that the NAD C-541i would be the best way to go, given budget concerns, a number of good reviews and a top-place finish in a What Hi-Fi? comparison with units from Arcam, Rotel, Rega, Marantz, Sony and Roksan. There's also the Shanling CD-S100, which I believe may be the same machine as the Music Hall CD-25 (although I've asked for advice on this in a thread on the Digital page here at Audiogon).
Also, I'm really tempted to find out if the merits of bi-amping are for real, with the addition of the NAD C-270.
Finally, although I said the cd player may be the weak link, the speaker cable is also vying for that title. I'm interested in the van den Hul CS-122, a 12-gauge silver coated OFC cable with a layer of carbon fibre that I've heard good things about.
I would say go ahead a get that NAD cdp because it would sure match well w/your other NAD pieces. (Also, perhaps one remote would be able to control all NAD pieces.) The spk wire most likely needs to be upgraded. I'm very pleased w/my VDH 102 interconnects. You may want to check out the CARDAS spk. wire also. I'm very impressed w/their Quadlink 5-c. If your C-370 has a detachable power cord replace it w/one of Subaraguru's DIY power cord. Very inexpensive and the improvement it brought to my system was amazing. (Was using a fairly decent aftermarket cord already, which costed quite a bit more, but the Belden wire in this kit was way superior.) Also, perhaps you may want to upgrade your power condition at some point down the road. Very nice system. Bill