Random stats, pick class based on that come up with a one or two sentence background, ask gm how much gold/points/credits i can spent on starting equipment and if there are any restrictions they have in mind for my background.
my last solo characters were an ex townsguard who helped his brother escape from prison, after his recruitment job for a local gang went side ways, so they fled the town and are now trying the adventurers live.
i think i'd be fine with also randomizing equipment and then coming up with a background, but i'd hate to fully randomize a character and end up with a line cook who owns nothing but a fancy suit and roller skates for some reason.