The triple threat Denons (D2K, D5K, D7K) don't benefit a whole lot from amping (they are incredibly efficient). All this talk about a powerful amp making them drastically better is a load of pure hyperbole. The benefits those people are getting is from the sound signature change the amps they use are adding to the Denon's own sound, which is personal preference and not actually real world benefit. A neutral amp vs a neutral amp will make the Denons sound pretty much exactly the same, whether the amp is $100 or $10,000.
I'd say just get a decent amp that can provide good, clean power to the Denons, and don't worry too much about cost. Say something like the Objective O2.
I'd say a DAC is more beneficial if you're going to hook them up to a computer.
So I would say the most beneficial product for the price would be something like the Fiio Alpen (E17), as it provides both good clean amping, and a good dac, without the bloated price.
Amping is good for headphones that actually need it to shine. The Denons don't need much.