"Click"-noise on note start

The best performance and value for money for audio DAC has to be I2S delta-sigma DACs - however they are hard to drive requiring 3 related clocks and bits have to be serially fed to them at Mb/s rates. 24 bit stereo at 48kHz sample rate for under a dollar in surface mount packages (WM8759GED, WM8524GED).
The Arduino isn't really fast enough to drive such a DAC (and do anything else useful!)

Other high resolution 5V or 3V3 ADCs are usually expensive and surface mount. LTC2642CMS is a fast SPI 16 bit DAC as an example, not very cheap, surface mount only...