They don't sell the V20 in my country, so I can't speak from experience. But I would expect that you would hear more difference with higher quality inputs (either lossless or high bitrate lossy) than with lower bitrate sources. Indeed a significant effect of a good DAC and headphones may be that you notice more difference between high and low quality sources. But at the end of the day what matters is do you enjoy listening to it.
Headphones recommendations are a minefield, because people have different ears and different preferences. What is your preferred style (in ear, over ear, on ear)? What is your budget? What are you going to be listening to and where (a headphone that's ideal for critical listening alone in your living room may be utterly unsuitable for commuting on public transport)? What is your preferred sound signature (neutral, bass-heavy, V-shaped...)? One person's ideal can be another's nightmare, so if you are thinking of laying out significant money (by which I mean significant to you) then I'd recommend doing some research and some listening to work out what you like before spending.