D&D 5E Preferred way to build your characters:

[Yaarel]

I was just about to suggest my system - randomly place the Standard Array:

Roll 1d6 to pick where the 15 goes.
Roll 1d5 to place the 14 among the remaining stats
1d4 for 13
1d3 for the 12
1d2 for the 10
And then stick that 8 in the loser spot.

The cool thing about a list of pregenerated arrays is, the size of the numbers vary as well as their locations. Yet each array remains roughly equal in value.

 

[Yaarel]

One system that worked out fair was for players to each roll the 4d6Drop array, but then all the players can choose from the result. So, if someone rolled high, all players can enjoy it.

 

[Hussar]

My favorite characters have always been concept first. Currently playing a Forge Priest that is riffing off a 2e character that I had played. My last character was a young woman searching for her lost father in Ravenloft (who wound up being a ranger).

I find that if I do class or mechanics first, my character never really finds a personality.

 

[the Jester]

Have you considered rolling randomly from a pregenerated list of arrays? This way all the results are both balanced and surprising.

That fails one of my character generation tests- "Does this method allow me to end up with a 3?"