It’s great that these classic games still make new fans even 30(!) years since their release! I can definitely recommend the Double Fine remakes of Grim Fandango, Day of the Tentacle and Full Throttle, and since Microsoft purchased Double Fine last year, they should be heading to XBox too (if they haven’t already.)
I actually envy you a little, being able to play these classics for the first time! Enjoy it, mate, they’re timeless!