I would suggest either a Cary 303 or Ayre cx-7. They are both really good players with their own virtues.
The Cary has a great midrange & bass signature that provides a slightly warmer than neutral presentation. The upper-end is good, but probably the players biggest weakness (IMHO). The top end is slightly smeared and rolled-off, but it does provide a wonderful musical presentation. Its a great bargain on the used market. You may also want to check on the 308T.
The Ayre is also a great value. You can find them used at the upper-end of your range. This player does so many things correctly. Its neutral with outstanding detail w/o being bright (great upper-end). This is a player I regretted selling. It did so many things right, but I just didn't find it engaging enough. This is probably more a function of my system & room dynamics than teh player.
You really have a lot of choices. If you are looking for a warm sound you should probably also look at the Jolida and Audio Aero Prima.
Good luck in what you decide. Please post your follow-up.
Also add to the list,
Audio Aero Prima
Jolida 100A w/underwood level 2 modification ($1800)
I admittedly have not heard the AA Prima, but have traded good feedback from warrenh and boa2 on here, check out the threads. A new one can be had at the upper end of your range. I have listened to the Jolida and it definetely has a much improved redbook playback as compared to the 2900 (which I have, and I am also adding a dedicated redbook player to my system as well, good choice I hope.) The underwood Jolida has a very open soundstage, good detail, overall, very very good. The Exemplar 2900 mod is also very good but I think it is close to $3K now.
Consonance cd2.2 needs to be added to list. I have one for sale as I am going to move to multichannel and will get a 2900 that is heavily modified as that is the only way it will be competive. I have owned many esoteric cdp's- All very good including: Electro EMC1mk2, Audiomecca Mephisto 2, Norhtstar m192 dac and transport and Res cd55 along with cd2.2. The cd2.2 at 2k is very competitive with others and at its used prices around $1300 it is a steal. 24/192,tube output via rca outputs with volume control. Tube and volume can be bypassed by using xlr ouputs. I was a rega dealer as well and all players above better the Jupiter-thoough a fine player-and the Jupiter betters the Arcam's and Jolida players in comparisons that I did in my store...Have not heard the naim but would say it is going to be in a higher league as well...E mail me in interested in a deal on my player...Scott