The character class in The Elder Scrolls system is just a configuration of Major and Minor skills. 7 out of 21 skill are chosen as your Major Skills. There are various default possibilities to choose in the game, but it's just as good to create your own, new class from the beginning.
You want your Major skills to be set in a way that lets you level-up with the right pace. All monsters in the game develop just as you do, so you should always think twice before deciding to advance a level. In fact, the common thought that your Major Skills should be the ones you use most frequently isn't at all right. If you choose skills like Blade, Acrobatics, Destruction etc., you'll find yourself in a point in which you'll know you've leveled too fast and everyone around can beat the crap out of you. You should always control the tempo of Major Skills' growth, combining both useful and fully controllable skills in them. You don't want the difficulty to raise too high, but you have to be able to actually level up when you decide that you're powerful enough already.
Remember about the multipliers that we talked about in the character creation introduction. Major Skills rise faster, remember about it while trying to build up your multiplier. If you want to focus on melee combat, you'll be needing a lot of Strength. In order to raise it, you have to practice skill that are governed by it (ex. Blunt). Remember that the multiplier is the one factor that lets you actually get an advantage over the rest of the world when you level-up. Keep in mind that if you want to get such great multipliers as three times x5 in one level (yup, it is possible), you have to practice the right minor skills also.