The Thieves are some of the best games ever made. I'd play them in order, although you could do Deadly Shadows first. The graphics of the old games should not be a problem if you are OK with old games in general. Other than iffy graphics there is nothing really old-fashioned about the old Thieves that should cause a new player too much trouble.
I'd definitely not just play Deadly Shadows though, the first two games offer things that Shadows doesn't. Metal Age in particular is a glorious achievement and deservedly sits at #2 in the NathanH video game ranking.