DHIADW is a good place to start - many think that is their best work, but I'd suggest going all the way back to the beginning and listening to Sanctuary right up through TGE just so that you can see how Warrel and his band has progressed. If you want to cherry-pick songs, two of my favorites are the last 2 songs on POE - 42147 and The Learning.
Most NM fans actually love the vocals, since that is a big part of what separates them from all the rest of the metal bands - a heavy band with actual "singing". I like a lot of growlers and screamers, but I always go back to NM because I get that extra level of melody and songwriting with lyrics I can actually hear sung.
Take caution with this board and don't take things personally - a lot of opinionated people and a lot of sidetracked food porn, but right now this is the best place to keep up with things.....WD himself usually pokes around adds some commentary.