kali77,
Are you considering this a starting point or an end point? Trying to build one system that covers both portable and home use can be a tricky task especially given what sounds like a preference for a large open soundstage which suggests open headphones. On the go open headphones are going to do two things that are bad, one they will offer no isolation from the outside world so you'll have the urge to turn up the music louder than you probably should and two, they will leak sound like a sieve annoying the crap out of anyone around you.
While it's possible to drive headphones like the K702 or HD650 with a portable amp my experience has been that headphones like those work better with beefier home amps that are better suited to handle their more demanding loads. I've not owned the K702's but have tried the K701's (same thing, different color) on a few occasions and while I thought they were ok I never felt compelled to take it any further than those brief listens. If you prefer a more speaker like presentation you may like the HD650's but I've personally found the way they treat the soundstage odd and without an amp to really grab hold and take charge I've found that whole range of HD580, HD600, HD650's to sound a bit slow and underwhelming. My suggestion though would be, if you're looking for one headphone to do both home and portable that you go with a closed back headphone or an in ear monitor (IEM's). The ESW9's are a decent phone though ultimately I traded them because I found myself reaching for my IEM's over them even when in my home environment.
Here's another suggestion, if you're intent on just one phone for both home and portable avoid harder to drive headphones because regardless of what's said I personally think you'll only hear a fraction of their full potential using a portable amp. When I downsized and went to a mainly portable/transportable rig the cornerstone of my system became my Pico DAC/Amp, I listen mainly at home or at work via a computer setup and the Pico has an extremely high quality and well executed USB DAC which was the real selling point for me. The amp is quite good, relatively neutral and transparent for a portable amp but at it's heart it's still a portable amp so I've typically steered away from harder to drive phones. Because my phones are typically not that hard to drive I don't tend to bother with an amp when out and about as I don't feel the sonic advantage of amping my iPhone outweighs the inconvenience of the added bulk of an amp. I don't really listen much on the go though so someone using them more in that situation might be inclined to want more.
A big question I have is what kind of system do you intend to listen to at home? Is it going to be thoroughly iPod based or do you intend to use a computer or CD player? That decision could determine what you get as far as an amp goes. If you're going to use more than just an iPod you could consider a DAC/Amp combo that could be used as an amp only with your iPod or as a DAC and amp with a computer or CD player. Of course what type of transport you use would also determine your connection needs, there's a plethora of USB DAC/Amp's out there, some, like the NuForce uDAC are very reasonably priced for the sound you get but with a USB DAC you're limited to USB input for the DAC so if you need coax or optical you have to look at something a bit more elaborate and typically larger.
$500 sounds like a lot but in reality it's a rather limited budget to build a high quality system around. I have this urge to suggest that if you're main listening will be done at home and you have a preference for open headphones that you may be better off building a decent home system and getting a pair of closed phones or IEM's for use on the go. You're standing at the edge of the rabbit hole about to take the plunge, a lot of money can be spent so I'd suggest you do lot's of research before making the plunge. If you're anywhere near where a meet takes place you should go, a meet isn't the best environment to listen and come to definitive conclusions but it can give you good idea of what you want to pursue and listen to further. Of course the other route is to increase your initial budget significantly and go straight to the top. First, go to your audiologist to get ear impressions made, send them to JH Audio and get a pair of 13Pro custom IEM's, for me these are audio nirvana, just about the best audio I've heard and I've heard a lot. The crazy thing is you can throw them in your pocket and they sound incredible straight out of an iPod but scale extremely well when used with higher end gear. Yes, the 13Pro's are about double your budget but in the long run I'd bet you save a significant amount.