Assuming that you have a little luck at the beginning of the game as far as picking up treasure, your character could easily be high-level within a few weeks of stepping out of Privateer's Hold and not have to fight anything. On the other hand, your character could spend years of game time gaining just a few levels. Skill placement is the key. The cold hard facts of life in Tamriel dictate that you will live or die by which skills you place in which slots.
For ease of skill development, nothing beats the schools of magic. You can sit in a nice, comfortable tavern room and sling spells for a few weeks, resting to replenish your magica, and become an instant machine of death. A High Elf with Critical Weakness to Parlysis, Restrictions from a couple of materials and 3x Magica is ideal for this. The 3x Magica and Critical Weakness essentially cancel each other out by leaving the difficulty dagger at about 1.0x (normal skill advancement). The material restrictions will drop the dagger to about 0.5x (more or less). Make some cheapie practice spells in a spell-maker and you're set. Spend a few days doing the easy quests for the Mages Guild to get access to the item maker and everything else will take care of itself.
If you'd like to make life really hard for yourself, create a Linguist character. Stick those language skills in your Primary and Major slots and leave all of your weapon skills in Miscellaneous. Got any idea how few Daedra are running around when you are 2nd level? The nifty thing about this type of character is that you don't qualify to join any guilds, so getting training in those Miscellaneous skills is out of the question until you increase some of them by 15 or 20 points or pay the exhorbitant fees of the temple trainers. If you'd like to make it even harder, give your character some really nifty, but useless advantages and no disadvantages. Try it when you're feeling suicidal.
Critical Strike is a must-have skill. It allows you to do more damage with your weapons. Though it will develop on its own, starting it off in the 20's or 30's gives you an edge at the beginning of the game.
Most of the "canned" warrior-type classes include several weapons in the Primary and Major slots. I've found this to be more of a hinderance than a help. Yes, it allows you to immediately use any nifty weapon that you come across. But on the other hand, you have to continually swap weapons in order to develop these skills. Pick your favorite weapons type and put it in as a Primary or Major skill and your second and/or third favorites as Minors.
Putting one school of magic as either a Primary or Major skill will allow you to immediately join the Mages Guild and get access to the spell-maker. Even if you do not have Increased Magery as an advantage, it's a good idea. Mysticism (for the "Recall" spell - you'll need to practice a lot with a cheap "open" spell to get the casting cost down to reasonable levels, though), Thaumaturgy (for "Levitate" and "Water Walkking"), Alteration (for "Water Breathing") or Restoration (for healing-type spells) are good choices.
Some skills should not be included unless you have a specific purpose in mind: Medical (which will develop on its own), Mercantile (which you can develop by selling off your goodies), Running/Jumping (which you can develop on your own) and languages (can be trained at the Mages and Fighters Guilds if you need them) are wasted in skill slots except for role-playing purposes.
You might consider taking Archery as a minor skill. Humans will certainly be trying to make a pincushion out of you at every opportunity. It's nice to be able to return the favor, but not critical.
Swimming and Climbing are recommended as Minor skills. You will need them, but won't be using them often enough to justify their inclusion in a Primary or Major slot.
Unfortunately there are just too few opportunities to make effective use of the Pickpocket skill in a role-playing sense. It might be worth it if you stood a chance of grabbing something worthwhile. But at a maximum of 5 gold per attempt, it's just not worth the effort. Yeah, you can wander around town and pick the pockets of the townies. But if you're that hard up for cash, go pillage a graveyard. The best use of the Pickpocket skill is to get you into the Thieves Guild.
Developing your Lockpicking skill might be an early priority, even if you don't include it as a skill pick. At higher levels you encounter locked doors with greater frequency. Unless you're willing to wear out your knuckles, break weapons or burn off your magica, you'll have to pick the lock. There is some evidence, however, that increasing your Lockpicking skill also increases the chances that you'll encounter a locked door.
Streetwise and Etiquette are "nice-to-have-but-hardly-essential" skills. They'll help you a little in your dealings with townies or nobles by modifying the reaction roll.