Minimum base stat for a good stat distribution

It depends on two things.
One: Are you trying to play arena? The tier list on Gamepress is meant for offensive arena, and it's based on a unit's base stats alone, not how good they are. Outside of arena, a unit's stats don't need insane stats as long as they can get their job done.

Two: Is the hero in question a balanced hero or a min-maxed hero? Heroes like Ayra, Karla, and Owain would prefer all of their stats dumped into attack and speed, and don't need their defensive stats as much. Dragons and Armored units prefer their stats in the defensive stats, and as long as their attack isn't abysmal, it's ok to sacrifice attack and speed stats in exchange for defensive stats. Other heroes might want a balance of the two, and those heroes are the ones used for modes where you need to fight large amounts of enemies in a short amount of time (Tempest, certain story maps, etc)

For offensive units, I'd say the minimum stats for attack and speed would be around 34 or 35 for both attack and speed, before adding in the weapon.

For defensive units, I'd say that 28 or 29 attack is the minimum, speed isn't important, and the defensive stats should be at about 32 or higher.

For mixed units, all stats should be above 27 or 28 at the least.

at neutral imo,
33 atk is standard, lower than this you will have quite hard time on some bulky units.
35 spd is standard, pretty flexible, you can just ignore it and put QR, it is a good value to deny double, and actually still manage to score some double if you get the +spd one.
30 def/res is standard, still taking a quite bit of damage, but still manageable. 30 res is also quite good for ploying.
35-40 HP is a good amount of HP imo, it's normally enough to survive most battle, provided youre not getting doubled.
over 45HP is what I start to consider a waste of points, unless you have specific prf weapon/skill, like aversa.
or if you just want to built a panic ploy user then above 45HP is nice.