Welcome Julie,
It's been mentioned a few times already, but knowing the room set up and your musical preferences would help a lot.
The Axioms can stay for a while, you could've done a lot worse. You mention a lack of detail, that may be partially improved by using some decent speaker wire. CD Changers are notorious for providing convenience over decent sound; if you subscribe to the garbage-in garbage-out theory any problems emanating from the source will never be fixed downstream. If I was in your situation and had $1000 to spend I would allocate $350 for a good stand-alone CD player and $550 for an integrated amplifier, spend the extra $100 or so on some interconnect and speaker wire. Id buy the stuff used right here on the Gon to stretch my buck too.
Youll get a lot of recommendations, heres my two cents worth... I'll start with the CD player:
http://cgi.audiogon.com/cgi-bin/cl.pl?dgtlplay&1076520598&class&3&4&
Nice player, HDCD compatible too. Nice feature if you own some HDCD disks. $340 asking price
http://cgi.audiogon.com/cgi-bin/cl.pl?dgtlplay&1076090457&class&3&4&
I like this player lots, will mate nicely with a warm sounding integrated $425 asking price)
http://cgi.audiogon.com/cgi-bin/cl.pl?dgtlplay&1076022594&class&3&4&
If your budget is a little tight you'd do well to consider a 63SE. Sure it's a bit dated but a fine player for the money. $180 asking price
There are other CD players worth considering as well, this is a good starting point. Be aware that some players are more laid back sounding, not sure you want or need that in your system since what you're looking for is more detail.
As for an integrated, again there are a few options to consider. At the ~$500 mark two that are listed here:
http://cgi.audiogon.com/cgi-bin/cl.pl?ampstran&1076434310
YBA design at a fraction of the cost. I've owned one of these in the past, very nice unit. Yes it's a bit warm sounding but if you have a slightly more detailed/forward CD player it should match nicely. $575 asking price
http://cgi.audiogon.com/cgi-bin/cl.pl?ampstube&1076542209
Depending on your musical tastes a tube integrated may make sense. One of the advantages of a tubed unit is the flexibility, you can change the tubes and dial in the sound to your tastes. Tubes look cool too. $526 asking price
Some cable ideas, bear in mind cables can be negotiated a little more aggressively:
http://cgi.audiogon.com/cgi-bin/cl.pl?cablintr&1076612368&class&3&4&
http://cgi.audiogon.com/cgi-bin/cl.pl?cablintr&1076379016&class&3&4&
Silver will add detail, but .5 meter may not be long enough.
http://cgi.audiogon.com/cgi-bin/cl.pl?cablintr&1076687579&class&3&4&
Nice cable and ought to mate nicely with the CD/Integrateds mentioned above
Speaker wire Ill assume 8 is enough for your set up and you can use spades (better connection than most other termination schemes), but bananas are acceptable too.
http://cgi.audiogon.com/cgi-bin/cl.pl?cablspkr&1076216607&class&3&4&
http://cgi.audiogon.com/cgi-bin/cl.pl?cablspkr&1075894880&class&3&4&
So how would I spend your $1000 (I love spending other peoples money):
Music Hall CD-25 player $340
Audio Refinement /complete Integrated $575
Goertz MI2 speaker cable with silver spades $150
JPS Ultraconductor interconnect $70
With some negotiation you can probably get this stuff for $1000
Any one of these choices will provide a big improvement and will hold their value reasonably well. Yep, once you get into this hobby you'll be changing your system over time. Negotiate with the sellers, but be reasonable. Best, Jeff