I personally prefer the side missions to the main quest, so I'm going to give you a quick run-down of what I would do first.
If you like stealthy games:
1) Steal something, get caught and go to jail.
2) Proceed through the Theives guild
3) Kill someone
4) sleep, get contacted by the Dark Brotherhood
5) Do those quests
6) HAVE FUN!
A side note- when you get to a Dark Brotherhood quest concerning a dinner party, SAVE. You will want to replay it...
If you like to play as a warrior:
1) Get yourself a weapon, go and do the Arena missions.
2) when you get asked to help someone find themselves, DO IT. You will get loads of loot, not to mention certain other perks
3) Do the fighters guild, more leveling up
4) more fun
Mages:
1) Do the mages guild
2) Do the Arena
3) max out skills
4) WREAK HAVOC!!!
Tips of combat-
stealth characters: avoid frontal confrontation. If you can get a jump on someone, do it. Sneak, Illusion and Marksman are your friend. A stealth bow shot with the right set of arrows can take down anything. If you do get in a frontal fight, don't worry about running. One of my personal favourite memories of the game is running a complete Oblivion Gate without stopping to fight anyone. Just call me Speedy Gonzales
Fighting/Melee characters:
Try not to get involved in multiple combat. Whilst you ARE built like a tank, if someone gets a staggering blow in at the wrong moment, you WILL go down. Get yourself a decent, enchanted weapon, make sure it stays it decent condition and don't worry about slower, more powerful attacks. Generally, Blunt weapons deal more damage but are slower than bladed weapons, so go with whatever your combat style is. Likewise with armor, and as you won't have either the sneak perks of Stealth or magical perks of Mages, make sure you are carrying enchanted armor whenever you can. If you decide to take Block as a major, make sure to take Armorer as well, you need to keep your defences as high as possible.
Magic users:
Destruction! Your major damage skill is Destruction, so make sure you build on that. You can't take much damage unless you have some shields, so restoration is another great option. Again, you really want to take stuff down from longer range, but a mage with the right skills can play as anything. With alteration, you can boost your skills to whatever level you want (so whilst you could be a puny mage, cast a few spells and you can suddenly become an axe weilding maniac for a few minutes). Also, don't underestimate damage over time+ paralyse spells, it's a great tactic. Paralysis is also brilliant if you find yourself in a warrior circle-jerk, as it gives you time to run like hell.
Other than that... Have fun
