Well, my experience is not unlimited by any means, but I would recommend you start by listening to an FMJ CD 33 at your local Arcam dealer. This is the best Arcam has to offer, but will give you a very close idea of what you would be getting with a used FMJ CD 23, though that would still be a little over your price-range even with patient shopping. Arcam does have a quite distinct sound - it is forward to be sure (as though you were sitting up close at a concert). For the money, I actually somewhat prefer the Linn Genki, but this has a much more laid back sound. To me, its sound is also smoother, more musical and particularly more analog in character, which is my preference, but not everyones. The good news about the Genki is that it usually goes for between $825 to $925 (don't let the current offerings on Audiogon fool you - these are over priced by historical standards). Others here will have equally good suggestions, and check out old threads.
But don't buy a Genki, or anything for that matter, unless you have heard it. Depending on where you live this can be tricky, but it is such an important point. Some people here and elsewhere make bold, sometimes trendy recommendations when in reality you may find what they like to be very disappointing. I for instance have been quite under-whelmed by several brands that others rave about, e.g. Mark Levinson (WAY over priced for what you get) and Wilson Watt Puppies speakers (brightness that hurts!). It is your money and they are your ears, never forget it.
One more thing. If possible, compare CD players in the same store using the same electronics and speakers. In fact, if it is a store other than your Arcam dealers, take in your CD 73 to compare with that shop's gear. Otherwise, it is really impossible to do an accurate comparison. Finally, when it comes time to buy used, do it safely. Buy from people well established on Audiogon or VERY well established in selling audio equipment on ebay. When in doubt, insist on using Escrow (escrow.com). My preference is buying from audio shops that list on these sites, though I certainly don't do this exclusively.
Hope this helps. Welcome to this wonderful world of good music reproduction. I hope it enriches your life as much as it has mine.