A desktop amp that I can personally recommend for the HD650 is the Purity Audio Caliente. The performance of the Caliente with HD650, to my ear, surpasses that of the HD650 with a PPA with discrete buffer and 24V STEPS PSU, with a high-bias M^3 with Blackgate power caps and 24V STEPS PSU, with a Mapletree Ear+ Purist HD with high end tubes and power cord. There is a lot of synergy between the Caliente and the HD650 for $370 CAD + shipping which yields an audio result that is simply stunning.
Lengthier Head-Fi reviews of the Caliente are linked on the Purity Audio website,
Purity Audio under the "Reviews" link in the navigation header on the main page.
This combination of amp and phones is so involving and revealing simultaneously that you'll really want the best source material and upstream audio path within your price range to get from it what it can deliver. I can personally recommend the upstream in my signature as delivering excellent SQ. In a more compact and convenient form, the source in my Bedside rig is also quite good (5.5G iMod + iMod VCap Dock using VHAudio caps), but not up to the fine quality of the upstream in my main rig, and for almost the same amount of money. Where the money goes in the iPod/iMod source route is portability, versatility, convenience. If non-portable, highest SQ is the goal then the money will be better spent on desktop, wall-powered source gear.
An iPod is a terrible thing to waste, and, with a decent Line-Out Dock (a cable) and a decent portable amp, you'd have yourself one fine-sounding system to use the HD650 with while you line up your more expensive amp and source purchases toward your ultimate rig.
Here's a "sweet-spot" suggestion for a modestly priced and very decent source and amp which could be used with the iPod as an amp and with a computer (via USB) as both source and amp is an iBasso D3 Python - a combined DAC/AMP which has been getting high ratings from folks whose ears I trust (HiFlight, mrarroyo, jamato8, headphoneaddict). For about $200 it provides a USB DAC which HiFlight likens to the HeadRoom Ultra Micro DAC - which is my main source and I LOVE it. It also provides an amp which has been compared quite favorably to amps costing more than twice its price. So, immediately, for about $200 (plus the cost of a decent Line-Out Dock cable) you could be pretty happily enjoying what you've already got while strategizing a desktop rig. I don't own the iBasso D3, so I'm bringing this up from what I've read and how it could fit into your strategy for getting yourself from what you have now to how you could grow that into a dream desktop rig in the future. I highlight the D3 based on HiFlight's rating of its DAC as on par with the Ultra Micro DAC - which, with a computer for USB audio and a desktop amp could get you to a very nice step toward a decent desktop rig with the desktop amp of your choice.
I've got one of the early (and least fancy and least expensive) ALO iPod Copper dock cables which I use with a 4GB iPod Nano that I got as a "Five Years of Service" gift at work which sounds surprisingly good when the portable amp is well-matched to the phones. I'm the VERY happy owner of an RSA SR-71A for use with Yuin PK1 at work and with HD650 at home (unfortunately all sold out now), BUT from what I've been reading about the RSA P-51 Mustang (still available), it sounds like it'd be a very good portable amp for use with the HD650 (likely at home) as well as with a more portable phone (just to pluck one out of the air, the Yuin PK1) on the go.
So, really, depending on what you'd like to listen to now and how long you can wait while you accumulate more pieces of a higher-up desktop rig, you've got a very nice variety of choices you can make.
(A)Start building a desktop rig now using the iPod as source with a desktop amp and HD650. For that I'd recommend a Caliente amp. There are so many "What amp for HD650?" threads right now, that you don't have to look much to find lots of suggestions on which to do follow-up research on your own. And you'd likely need a mini-to-RCA cable to interconnect the iPod and amp.
(B)Straddle desktop and portable with an iBasso D3, which would allow the use of the iPod (with Line-Out Dock cable) as source, and a computer as source (using higher bitrate source material like wave files or lossless files) via USB. HeadphoneAddict has started a thread of DAC/AMP reviews for more suggestions and reviews in this category.
Using this buys you as much time as you need while you research and strategize a full desktop system.
(C)Complete a portable rig now with the portable amp of your choice and use that while you think more about what you'd like your desktop rig to be. Skylab and mrarroyo have started threads where they review large numbers of available portable amps over a wide range of prices.
(D)The Quaternium Quid of your choice.
It really comes down to your goals (immediate and long-term), and your timetable/scheduled budget as to which path you'd like to take from what you've got today to what you'd like to have down-the-road.
