You can always buy a great pair of headphones now that fit in your budget and later build/buy a quality headphone amp to further improve sound, Just do it in stages.
Seriously though headphone amps are possibly the cheapest and most enjoyable DIY audio projects you could attempt, if your half decent at soldering and have a bit of free time you will surprise yourself with what you can make.
This site is full of superb DIY headphone projects.....
http://headwize.com/projects/index.htm
So many different circuit designs and topologies to choose from its unreal. I'd really like to build a cute little OTL Tube headphone amplifier to replace my current single ended tube headphone amp.