There are certainly ways to optimize builds, if you want to do that. I have several ideal builds I play that look rather similar in actual major skill selection, but vary based on which specialization, race, birth sign, and how I choose to play it.
For me the most powerful is usually a combat spec with magic for backup, or a mage spec with strong combat skills. Just wade in and kill everything.
I have also played stealthy archers with maxed Alchemy skill that could fire off a single arrow from hiding and then just wait for the poison to do the job. Or stealthy mages who sit back and crowd control the foes and send in summoned creatures for the kill. Or war mages who just blow everything away with powerful destruction spells. And hybrids of all three.
Here are some basic rules for making decent character that doesn't level too fast and gives you the option of getting good attribute bonuses at level up:
Use a custom class. Pick no more than two skills from any attribute as majors. My personal approach is to pick one skill from each of the 7 attributes. Always pick Endurance as one of your two favored attributes, since your character's health is based on Endurance (and cumulative health increases per level as well). Make your primary killing skill(s) major skills. I usually go with Blade or Blunt, Destruction or Restoration, and Marksman as majors. I NEVER take Conjuration, Alteration, Alchemy, or Athletics as a major, since they level you so fast.
Now you can certainly play any way you like, but you did ask. Here's a typical build for me:
Majors: Blade, Block, Destruction, Light Armor, Marksman, Mercantile, Mysticism.
Favored attributes: Endurance and Strength (even for mages - got to carry the loot out somehow).
For an archer-type:
Spec: Stealth
Race: Dark Elf or Wood Elf (though other races are OK too, those are ideal).
Birth Sign: Thief, Warrior, or Mage. With Dark Elf, the Lord works too.
For a mage type:
Spec: Magic
Race: High Elf or Breton
Birth Sign: Mage or Atronach. Atronach requires some expertise to play.
Warrior type:
Spec: Combat
Race: Nord, Redguard, Imperial, Dark Elf. Orcs if you want, but I can't get into them.
Birth Sign: Atronach, or Warrior. Atronach here is more for the 50% spell absorption more so than the extra magicka.
Hybrids:
Spec: Any, though I use this to counter the race's strengths. I.e., for a Nord, I would spec Magic, for a Breton, I would spec Combat, since this is a hybrid build that needs to be good at both.
Race: Combat-oriented = Dark Elf. Magic oriented = Breton. I have also played very effective hybrids that were Argonians and Imperials.
Birth Sign: Mage or Atronach. If you are going to be a part-time caster, you need some extra magicka.
Those are some suggestions based on what works for me. You may not like those builds at all, so feel free to try your own.