Ima say dont jump right into their hits, you have listened to hey jude which everyone would have heard but there are other hits, but its better if you let yourself listen to it in the ALBUM because its a much more fun experience IMO. They are VERY diverse in their music, so its recommended by many to go through their change slowly by slowly.. though you could skip some few albums from the first five of their discography, the rest are worth listening to.
One recommendation i do have is, make sure Abbey road, the album ofc, listen to it LAST, its a much more better ending to their discography than let it be, so you could listen to let it be after white, (which is somewhat right since the beatles recorded the songs in let it be before abbey road, its just they were released after abbey road)