HD650 comes with a 1/4 inch plug and a 1/8th inch adapter. I doubt the adapter makes a noticeable difference. Likewise, I'd hold off on the unnecessarily expensive recabling jobs because again the difference will not warrant the cost at this level.
Bottlehead kits and prebuilt amps are sold here:
http://www.bottlehead.com/store.php
I'm actually not 100% sure what the best place to get Millet Hybrid kits is at the moment, but look through the DIY forums, and finished amps do come up for sale quite often.
The HD600 is also an option. I think it does quite a bit better than the HD650 on lower-end gear. The HD650 scales better and from a good amp will offer detail, soundstage, and instrument separation that the HD600 can't quite match, but from less than stellar gear the HD600 should outperform it. The two headphones are quite similar overall, so really it's a matter of what works best for you. There are also different production versions of each, and... well it's complicated, but here's a good review site which I will take the opportunity to
shill pimp:
http://www.innerfidelity.com/
Basically, you'll find headphone measurements as well as subjective reviews, so it's a bit more trustworthy than your average review site, and will give you a good starting ground to make sense of the general mess that's the headphone hobby today. A little bit of knowledge will spare you some bad financial decisions and will really help out in the long run, so it's a good resource, and there others like it - just take the time to look.
Lastly, when you do decide to upgrade, remember that the source is just as important. Garbage in = garbage*gain out. It doesn't really matter when you don't have the resolution to hear it, but since headphones offer better detail per dollar than speakers, you will notice a bad quality source more quickly as you start to upgrade.