*disclaimer: the roleplay and freedom too are important parts of defining your character.*
But, for this game series, the skills make the player. The original idea is fantastic, but it's never been pulled off perfectly. It's simple: Do stuff, and get better at it. Practice makes perfect. Practicing magic makes you better with magic. Practicing swordplay makes you better at swordplay. Practicing singing makes you better at singing.
By this logic, all the games have to some degree failed. In the first four you'd level up and pick which attributes to get. It shouldn't work like that. Lifting should make you stronger. or, well, exercises involving strength should make you stronger. The multiplier system was awful to play with and illogical. You'd have to try and get good multipliers, and if you'd had a spread of modifiers (let's say everything is x3) then it wouldn't carry over next level. The skyrim system of perks as the primary means of getting more powerful? Absolute heresy. If I were to attain five levels of smithing and ten levels of archery, skyrim's system would only allow me to get better at one of them per level. Plus the gains were very... unatural. You'd get leaps of 20% more damage or suddenly knowing how to make dwarven armour.
What we need is a true system of practice makes perfect. No [censored] multipliers or all-powerful perks. Less arbitrary confines (can't use the spell at Illusion 49, can at 50) If you fight unarmed, your kung fu becomes strong (especially if you attempt a good variety of skills) . If you cast a lot of illusion spells, you get better with illusion spells. If you do a lot of backbreaking, your endurance goes up. If you attempt a lot of strength feats, that goes up. If you subject your mind to the arcane, your intelligence goes up. If you fully push the limits of social skills, your personality goes up. That should be elder scrolls.
Perks are a good idea. Perk perks by the way, not skill trees. Character defining things, like if your character is willing to be brutal when fighting or if they are to stay honourable. If they adopt a certain poise in social situations. If they're able to taste the ingredients in a food or the components they think a potion is made of. If they can use their personality in a fight to misdirect or intimidate an enemy. even simple things like if they're attractive, have an innocent face, look like a bruiser etc (I'd imagine such things would largely be chosen at the start of the game. Though you could change that through creative use of restoration, illusion, a bit of washing,alchemy, battlescars, gaining rippling muscle, deals with daedra...) These need not be leveling up perks, and perhaps they're not all 'all good' either (Appearances may gain unwanted attention, and fighting with too much or without enough restraint should raise a few eyebrows) so maybe you could take them when the time is right, not when leveling up. (knowing how to armour in the orcish style should be gained from a tutor, a book, or the study of existing orcish armour)
But, I sincerely hope that this is how the elders scrolls will roll. It's a natural system.