There are some truly excellent DACs out right now in the low budget range. I'd opt for the SMSL Sanskrit one for $99, or the Topping E30 for $130 (I'd go for the Topping, myself).
As for a headphone amp, the various versions of the THX amplifiers are the best right now and they're pretty affordable. The one from Drop is now $300, Monoprice and SMSL also carry versions for around the same price...all sound pretty similar. If you want to go cheaper, the JDS labs Atom is fantastic, too.
You're not going to find a huge difference amongst well designed DACs unless you get one that is technically inferior (multibit) which adds some 'warmth' to the sound. Nothing wrong with that, if you're into it. Myself, I'd just put a tube in the system somewhere if I were looking for something to add depth and warmth to the sound.
The Soncoz LA-QXD1 seems like it'll be an absolute beast of a DAC around $200, but no remote (if you care about that). It's also balanced. That would be the next step up from the Topping E30, though I can't say the improvements are audible at this level of performance.