In that case, if you're deat set on the Pico (and I'd get that instead of the Predator) then the HD600 or HD650 will be very nice for it. I'd go with the 600; it's a bit more neutral and easier to drive. The HD650 really does need balanced drive to show what it can do. But, at the same time the HD650 has a warmer tone. I find that a lot of older stuff tends to be rather thinly recorded, and the HD650's greater heft and warmth compensates for the dated production. The HD600 will show you more of what's on your recording, and the HD650 will impact more of its own character to the recording. But, don't get the HD650 without an amp that can hack it! It can sound dreadful on an amp without enough juice. The HD600 is a lot more forgiving in that respect.
With the HD600, the Pico can be the amp/DAC on the move and will be good enough for stationary purposes to start with. Not sure about how well it handles the HD650, but I've heard positive things about it.
Later on, when you want to throw more money into the rig, I would suggest going balanced. If you want to stick with Headamp (and there's no reason why you shouldn't, Justin makes some serious stuff), you can get a GS-X, a balanced source, and a balanced cable for your HD650/HD600. That will be a top-tier rig and will be definitely worth the investment - but it will also be a pretty hefty investment. Still, one thing at a time.
You can also try some electrostats - a Stax 2050 system or a SR-005a system will do the trick nicely. Yes those 003 headphones look puny, but don't be deceived - they sound killer and have serious bass. the 202 headphones are different - they are very airy and expansive, but a bit leaner/more analytical than what you're probably used to. They sound terrific on well-produced recordings, but badly-produced ones will sound pretty painful. The 005a system will be more forgiving.
In either case, you will need a good source, since an electrostatic system is a lot more revealing of source quality than a dynamic system (in general).
You can also play around with some vintage gear. A normal-bias Stax Lambda, together with a transformer box, is one of the best high-end headphone bargains out there. But, I'm not kidding when I say "high-end," and you
will need a good source for it, as well as a speaker amp that can drive the transformer box. All of this doesn't have to be expensive, but it will take some effort in terms of tweaking and component matching before you get the most out of it. Be careful with buying used Lambdas and make sure you get a pair in good working order. They tend to be reliable when they're taken care of, but you never know. You can also try a K340. This will absolutely need a beefy amp to drive it, preferably a tube one. There are also different-sounding versions of it out there, generally called "bass-light" and "bass-heavy" versions (though there's more than just 2). I'm not sure how much of the difference is due to original design or due to how the headphones have held up over the years, but bass-light pairs tend to sound really, really good out of warmer, euphonic tube amps. I had a $200 stock K340 out of a $200 old tube amp, and it was one of the best rigs I've had. Fine wine taste on a beer budget, so to speak. But, K340s are old, and are in different conditions, so once again you'll have to be careful with what you're getting.
Anyway, just some food for thought...
