I mean no disrespect to the OP but this question is like someone asking where to start with the Beatles or Led Zep or Pink Floyd. You can start anywhere, its all amazing stuff. Dylan is probably the greatest songwriter and lyricist of all time, and he's a bonafide poet, probably one of the finest poets of the last half of the 20th century. sure there is nothing better than the actual song and music, but you take his lyrics and they read as genuine poetry. plus the OPs question hard to answer because Bob has been recording and making music for so long. His first album, an album of folk covers, came out in what 1962 or something and in 2009 he released a Christmas record and a studio record, plus the Bootleg stuff he puts out seems to come out every single year, a new record of songs from the vault.
He is the type of guy, like the Beatles, its impossible to overstate his importance. His impact on culture at large, not just music, is massive.
His catalague spans everything from blues and folk, to rock and swing, and everything in between. He had a political phase, and a country phase, his most famous 1963-1975 or so was all over the place, a phase in the 70's where he donned white makeup, he renounced his jewish faith and became born again in the 80's, the late 80's and much of the 90's he was largely forgotten, or as forgotten as someone like dylan can be, and his last 4 records have been as acclaimed and beloved as any of his 1960's music.
It all depends on what you like. You cant go wrong with Freewheelin 1963, Times and Another Side both from 1964, Bringing it all back home, and Highway 61 from 65, Blond on Blonde 66, John Wesley Harding 1967, Nashville Skyline 1969, Blood on the Tracks and Basement Tapes both 75. Thats the basic stuff people refer to when they talk about Dylan, thats the classic Dylan. Although as I said, he's as important and vital as he was back then.
Id check out a show on his current tour if it hits the states. Ive seen him 3 times since 2001, including a show the night we started the war on terror and started bombing Afghanistan. And its a real blast. Its funny he plays a great set, but he's done and out of the venue by like 930. Pretty crazy.
Whatever you do, listen to as much as you can of Dylan, Start anywhere. Its like asking where to start with Shakespeare or something. Whereever you begin and start, you will be getting your mindblown with some of the greatest art of the 20th century.
Part of the reason why Dylan is so respected by so many people, including myself, is that he is the ultimate rebel. He has refused to listen to or cater to either fans or critics. He wrote political songs before being political was popular among the hippie counterculture. And when people started becoming political and wanted him to speak out more, and become something he was not he crashed his motorcycle, either on purpose or by accident to get away from his record label and contract. He then started writing personal non political songs. He went country before it was popular for folk artists to go country. And when everyone started going country he changed again. Pearl Jam made No Code to lose fans, but they no doubt feel its a worthy album. Dylan put out an album of stuff he considered bad songs and a bad album and released that all to lose fans and get the critics off his case. I cant think of another musician who has ever done that. Being born again, and then releasing some of his strongest material in his 60's and 70's all are examples of someone, an artist, who refuses to follow any marching orders from anyone other than himself. That is something that is so rare and is why he is a hero.
How many other musicians do you know of who won a Pulitzer, and have a large base of people who are now hounding the Nobel committe to award him the Prize in Literature.
I think it was Bono who said no matter where you are in life, there is always a dylan record to help you map the terrain.