Not sure what ALL I'd do....but I'd start with this:
A very small set of spells every spellcasting class had access to (different for each class). Sub classes would add to that, so that different flavors of wizards were actually different from each other. I understand this would likely not be popular, btw.
I'd put A LOT more into clerics being different depending on what they worshipped. Why do they all kind of get the same powers? Again, this might not be popular, but I think moreso than the above.
I'd convert the paladin into a holy warrior class whose powers were, again, dependent on what they worshipped. Holy warrior is probably not the right name, more like "idea warrior"....this class does what it does for reasons, not for fame/fortune/whatever.
All fighters would have access to some set of cool things the rules say they can do.
I'd do something with the old skills thieves used to have, seems all jumbled now.
I'd go with lineage, culture, background. Background would be the most important thing for what skills you start with. I'm not sure how the heck I'd handle how an orc is different from a dwarf. Like, I think they are all people, but is appearance really the only difference? So complex...so complex. Culture would be where you grew up....like the city? or tribe? or underground? background is what you did there. Culture also gives you some skills (did you grow up travelling a lot? or in a farming area even if you didn't farm?).