I have been using a pair of C1s in my system for 4 years. I would highly recommend them.
I first powered them with a Gryphon Callisto 2200 integrated with ok result, and later switched to Linn's Klimax pre and power amps for better control. I also went through many different source equipment, and now the C1 is the oldest and the least expensive link in my system, and yet I do not think I have explored its full potential. I do not know Boulder 865 well, but I would suspect---base on Boulder's price and reputation---it will be a good match with the C1.
C1 is so very transparent, capable, and neutral, my experience is that it can sound from dark to bright, smooth to harsh, all depending on associated equipment and cables. So you have to be very careful in selecting source and cables. As to CD player for 3-4K, I would suggest instead of CD player, maybe look into a music server. Many such devices claim to sound better than equivalent priced CD player, such as various models of Linn DS units, which may offer better value under $4k vs Linn's own CD players. I also found PS Audio's upcoming Music Wave Transport at $2999 interesting. But anyway, music server is only a suggestion, it is something I myself is looking into but have no first hand experience with.