Going to actual albums after all the great hits collections of his, you can not go wrong with the following
Hunky Dory 1971 (Art Rock/Psychedelic and Glam sound), Ziggy Stardust and the Spiders from Mars 1972 (Proto punk, Glam and straight rock), Station to Station 1976 (Funky and strung out), Low 1977 (Electronic Brian Eno Berlin Period), Lodger 1979, Scary Monsters and Supercreeps 1980 (Both post punk gender bending period), Lets Dance 1983 (If you like poppy hits), the Labyrinth soundtrack 1986.
Most essential - Heroes 1977 (Late), the best of his sparse Berlin period, Brian Eno sound, sparse songs and lyrics, David coming off the coke and hanging out with Iggy Pop, seriously way ahead of its time!
Most Bowie albums after 1983 are mixed, some good ones and some less good ones, all are worthwhile except both Tin Machine albums and the terrible Never let me down from 1987. The early albums, David Bowie 1967 is a piece of psychedelic sillyness and more comical than anything else, 1969's Space Oddity/David Bowie is mixed but again relies on the hippy stuff, 1970's Man who sold the world is good but not essential, there are some great cuts there like Width of a circle.
Pin Ups, Aladdin Sane, Diamond Dogs and Young American are also good albums but are for the more adventorous Bowie fan (I don't have them). The live albums David Live and Stage are best avoided.
Bowie is one of my favourite artists and I really love encouraging anyone to get into his music. To me he is a lot like Prince for his musical virtuosity and prowess along with his chameleon like changes from album. Like Prince in the 1980s each album changed fromthe last and he experimented with a different sound and he evolved with each one in the 1970s.
Two essential hits sets are David Bowie 1969/1974 and 1974/1979 as they have alternative versions and covers of songs not on albums like "Can you see me" from 1974 with backing vocals by an unknown soul singer called Luther Vandross and Bowie's version of "It's so hard to be a saint in the city", "All the young dudes' and a disco version of John I am only dancing.