Not sure about how many points, but I do like the idea of picking stats and powers and point values, at least to some degree. Besides, the dice roller here has sworn vendetta against me for some reason
As a thought, why not combine point cost and random though? Let me see if I can work through this thought and it makes some sense...
Select a base amount of points, have Players roll for additional points... for example purposes, say 250 base points, roll for more. Those are the points Players can use to customize the character with... Again for example... Set a "maximum" points per character of 400 points.
Player A starts with 250 points, rolls an additional 100. They can choose where 350 points goes.
Player B starts with the 250 points, rolls an additional 15 points. They choose where 265 points go.
The difference between those points (350 for Player A and 135 for Player B) and the 400 point cap are allocated by the GM. The characters would all be balanced with the same point spread, some would just know less at start up than others do about their characters. So Player A might have 50 points allocated by the GM, might be a little stronger than they think, or have some additional power. Player B would have more fun of discovering what exactly they are capable of.
Or... Just give everyone the max points and make it easy on you.