LucasArts is one of my all-time favorite game companies, in my mind they are still the best western game developer. Their variety and originality was unparalleled in the 90s. LucasArts defined my windows gaming experience in the late 90s / early 2000s, I still miss them. There's been the odd new game made by former LucasArts developers, but it's hard for those games to really capture that original charm.
Of the original SCUMM-based games, I've completed Maniac Mansion, Secret of Monkey Island, Indiana Jones and the Fate of Atlantis, Day of the Tentacle, Sam & Max Hit the Road, The Dig and Curse of Monkey Island. I highly recommend all of those games, they all offer that quintessential LucasArts quality. The original Maniac Mansion is a bit atypical with its non-linear flow and multiple endings though, so it's not really the easiest game to start on. Loom is also very odd, as it doesn't use verbs like the other games, I recommend it if you want a strange game.
I also recommend Grim Fandango and Escape from Monkey Island, but keep in mind these aren't SCUMM games so you'd either need ResidualVM or modern ports or the original PC releases.