Hi Matthieu,
What you need:
1) Raspberry Pi
Right now, I'd recommend the "plain old" Raspberry Pi B or B+. Namely, the Pi model 2 is still rather new, and not much of the hardware/software supports it. Well, it does, but there are glitches. Or, if you can wait a month or two, and see what's available on the SW and HW side then.
Right now, your best bet is Raspberry Pi B+ (see also below for the DAC). You'll also need an SD card (4GB Class 10 is OK, you don't need anything larger.
2) DAC
I'd recommned one of the DAC boards made specifically for RasPi, based on I2S protocol, like hifiberry, etc. Check the rest of the forum for recommendations, particularly here:
http://www.runeaudio.com/forum/compatibility-list-f11.html
Reason why I recommend a DAC custom-made for RasPi is that those use I2S instead of USB. Namely, to cut the long story short (and somewhat oversimplified), USB DACs don't work too well on the Raspberry, due to some hardware design issues. SOme people claim to use their USB DACs without any problems and with fabulous sond, but those are rare

Before buying a new RasPi DAC like I recommend, you could also try to use your existing USB DAC with Raspberry and RuneAudio, and see what you get. Most people get clicking, pops and other audible interference....

Anyway, those custom RasPi DACs are priced from €25 to €35, so it's not really that expensive. Just make sure that the DAC you are buying is intended for the Raspberry Pi model which you have (those for models "B" and "B+" are not really interchangeable). Also check what kind of audio out you want - these DACs usually have RCA analog audio out, but some also offer S/PDIF coaxial (or optical - i.e. TOSLINK) output.
You'll need a good power supply - preferrably 5V/2A (although 1.5A will also work).
Anyway, a good and complete hardware setup guide for RuneAudio can be found here:
https://github.com/RuneAudio/Docs/blob/master/docs/quick-start/rpi-hardware-setup.md
But, basically, what I wrote above should be enough:
1) Raspberry Pi (B+)
2) DAC for RasPi B+ (hifibery, iqaudio, etc.)
3) Micro SD card (for RasPi B+)
4) power supply with microUSB cable (5V/1.5 - 2A)
Install the RuneAudio distro as described here:
http://www.runeaudio.com/documentation/quick-start/quick-start-guide/
And you should be all set... Connect audio out from the DAC to the amp, and enjoy
Denis