For myself, I like to create characters that do meet whatever I consider the minimum requirements for effective play...and then from there I like to play with the formula, I like to create characters that have features one wouldn't necessarily expect.
I have two examples, one from back in 4e (where racial and level-up ASIs obviously work differently, but still) and one from 5e.
I have yet to play in a truly long-running 4e game, the closest opportunity I had ended abruptly when the DM had to shift their life around to care for an injured family member on top of their very young son. But every time I think maybe I have reached such a thing, I try to make a Dragonborn Paladin, 'cause I would dearly love to see this particular character evolve through from Heroic to Paragon to Epic.
But I find the "paladunce" archetype boring. Being sincere, rather than merely memeing, I
do consider myself something of an intellectual, and find it challenging at best to play a character that is of below-average intelligence. Instead, I crafted this particular Paladin to have a decent Int score. Nothing major, sure, but instead of dumping Int, I dump Dex, a stat that can be worked around. I also spread my stats out quite a bit--only 16 in my main stats (Str and Cha), using other means to make up for the reduced hit rate (high-accuracy At-Will, high-proficiency weapon, grabbing a magic weapon ASAP, etc.) This gives me the freedom to have respectable tertiary stats, including Intelligence. By taking a Theme and a Background that supplement skills, I can even get a character that matches the bonus of an Intelligence-focused character on a couple skills--favoring History and Religion. This gives a highly literate, philosophical Paladin: a man whose faith is very deep, but through substantial
active thought, rather than blind trust in the divine. He has taken various forms in various games (coming from nobility, being poor but raised up by the church, a relatively typical soldier who found profound faith, etc.), but the core personality has been largely contiguous.
Meanwhile, in 5e, I have a character I would
like to play in order to playtest a prestige class I wrote, Silver Pyromancer, based on the PrC of the same name from 3.5e. A Silver Dragonborn, who is also a Gold-blooded Dragon Sorcerer (explained as the intentional crossing of two noble dragonborn lineages with the intent of producing such a hybrid), in part
inspired by this image. Being the son of a noble family, he's a bit of a
bon vivant, but he also carries the expectations placed on nobility. As a result of his refined upbringing, he's not very strong (that's
day-laborer stuff!), but he is rather serious about both intellectual and religious topics in addition to his study of magic. Even though neither Int nor Wis is particularly valuable to a Sorcerer, they're both higher than his Con and Dex mods, because that makes more sense for this character.
So, like I said: I'll go for the "important" stat(s) that I need, but after that, I like to play--usually by making the character more widely-read, more of a thinker or sophisticate (whether that's merely superficial, highly focused, or generalized.) I also like to challenge a bit of the status quo, by making Sorcerers or Paladins that have a real brain behind the pretty face.