I'm new here and don't know much about much so I'll try not to make recommendations outside of the stuff I do have some experience with, but lets start with the source since it really helps to define the rest of the components... it would be easy on your budget to overkill on the amp and headphones only to have the limitations of your source revealed with astounding clarity.
Your music on the ipod touch should be 'Apple Lossless' encoding. MP3 or MP4 (Apple calls this AAC) files will sound pretty bad with an amp and headphones in the price range you're aiming at.
The best way to get sound out of the ipod touch is using line level out, not the headphone jack. There are ipod connector to RCA stereo jacks but double check that they work. I read somewhere the pin-outs on the 2nd Gen iPod Touch are different and old line out jacks won't work. You won't be able to charge your iPod while listening but with the great battery life they have this may not be an issue for you. A slick solution is to get the Universal iPod Dock and USB charger from Apple (I think it's about $80 for both). That way it sits on a cradle, will always be charged, and you have a line out jack on the back of the cradle and a remote control you can use while lost in audio bliss out of reach of your iPod. I think most desktop amps will have RCA in so you'll need a 3.5mm to stereo RCA adaptor cable if you use the Dock. Go for as short of a cable as possible, usually 1m/3ft. The longer the cable, the more signal loss you get before you even get to the amp.
As for amps and headphones, I'm just starting down that path myself so I'll leave that to others that have great ideas. A sensible plan would be to split the remaining budget about 50/50 between headphone and amp. If you've got $750 to spend total and buy the dock, charger and adapter cable, you've still got $650 for the amp and headphones, that will get you a great setup.
The CD Player to DAC/headphone amp is just a different way to spend your money and might work out better, but it also means you'll have larger gear in the bedroom and limited to loading and playing a disc at a time... not a problem at all for a hardcore audiophile but less flexible on the content side.