Errr...
The DAC you mentioned has a built-in headphone amplifier, so it's designed for listening with headphones and I believe it doesn't have the right output (Twin RCA/Phono line) for a hifi amp.
Amp: Denon are widely known as one of the leaders in budget mini systems with the DAB 38 (and 37 before it). They don't have the same name for their budget amps like the PMA510AE. Maybe it's OK for the price, I have no idea. I've had a budget Cambridge Audio amp in the past and these are very good--if you go to the shop I think you're probably looking in, you can hear both 😉
Tuner, no idea...sorry. It does seem a lot to spend on a tuner if your overall budget is 250ish. Are you using a computer or iPod/mp3 player as your source? Even if you've got a harddrive full of music, in most cases you still need a way to play the files.
On your budget, I'd be inclined to forget about the DAC (and tuner), plug your computer or iPod straight into the best amp you can afford and get some cheap but good quality used speakers off a well known auction site (or if new, the Wharfedale 9.1 if there are still some stocks left). If you want a new amp, Cambridge Audio Azur 550A would probably take some beating for 200 quid, with 50-100 for the speakers. Cheapo cables all round. If you get the music/hi-fi bug, upgrade your source and speakers later. Then if you really get the bug bad, spend 250 quid on a piece of wire and get a sparky in to fix your mains!
I'm actually listening right now to Spotify on my iPod going straight into a Creek 4330 (bought for 110 quid from a well known auction site) and JPW Sonata speakers (you can pick these up for about 20 pounds). It sounds surprizingly good. Almost as enjoyable as my other system costing 5 or 10 times more (depends if you include the computer/iPod in the budget--since I had those anyway!).
If you've got a normal DAB radio lying around you can always plug that into the amp if there's a line out socket on the back of the back.
If all this seems way too complicated...just get the Denon DAB 38, kick back and enjoy the music!