I think what TDH excels at is melody. I don't really find them all that "progressive", but I think if you appreciate good songwriting and realize a lot of their work is ambitious, you should like them. They've come to be my favorite band. You have a whole conceptual story that is supposed to eventually span across six albums. Act 4 just came out last year. You have The Color Spectrum which is a big melting pot of different styles and approaches, with each color being a different style of music. You also have Migrant, which doesn't get as much love as I think it should, as it's a more accessible rock, pop, alternative album.
I started out with Act 1, but I think you could start anywhere and enjoy it just fine.