Off of the top of my head, I would probably go 60% amp and 40% CD player. Naturally, others would disagree. In that price range brands such as Rotel and Parasound are bargains on the used market. I am partial to Rotel (having owned several Rotel pieces), and one could easily find a good Rotel power amp for $600 and a nice Rotel CD player for $400. I am assuming that a $400 CD player would be a step up for you, as you describe your current player as an El Cheapo, but that may not turn out to be the case - depending on what you have and what you replace it with.
There are many other possibilities, of course. For that same $600 you could probably find an older Bryston or McCormack amplifier, for example. Turning back to the CD player, an older Arcam or Cal Audio or Cairn unit could be had for around $400. A lot of people believe in putting most of their money up front - as in spending more on source/preamp components vs. spending more on amps and speakers. Again, if I were spending that $1K in your shoes, I would split it 60% amp and 40% CD player.
All of this advice is, of course, worth everything youve paid for it!
