If you give a follower a torch, they'll equip it in dungeons or at night, lighting the way for you.
It's also worth noting that, due to a bug, items picked up by followers don't weigh anything, meaning they can carry an unlimited amount of stuff. To get them to pick something up, switch to command mode and point at it.
When you start the game, you won't be able to fast travel to any of the major holds - Markarth, Windhelm and so on. If you're in a rush and don't fancy riding there yourself, talk to the horse and carriage owner in the stables outside Whiterun (or any city for that matter) and he'll take you to whichever capital you choose for a small fee.
Just because you don't want to read Skyrim's massive selection of books doesn't mean you should ignore them. Certain books give you a skill boost related to their contents - a book about armour crafting, for example, might boost your heavy armour stats. You don't have to painstakingly read every book you see, though - scan over them and look at their values. If they're over 100, chances are they'll give you a boost. Any less and they're just plain ol' books.
Travel to Markarth and head up the street to your right until you see a guard in an argument with someone. Agree to help him investigate the nearby abandoned house, and you'll begin the 'House of Horrors' quest. Complete it and you'll receive a powerful enchanted mace that drains enemies' stamina and magicka. The earlier you get this the better, as it's incredibly powerful.
Each magic type in the destruction school has a different effect. Fire is pure, raw damage, and more powerful flame spells will set other enemies in their blast radius ablaze.
Shock magic deals similar damage, but will also drain an enemy's magicka. Good for when you're fighting against mages and the like. Finally, frost damage drains stamina and will slow an enemy down.
You can actually speed up the laborious mining animation by dual-wielding pickaxes and 'attacking' the ore vein. You can find a unique pickaxe at the very top of the Throat of the World called the 'Notched Pickaxe'. This increases your smithing skills and does shock damage to enemies.
Whenever you find an enchanted weapon - one with a status effect, like 'Orcish Sword of Flame' or 'Dwarven Sword of Leeching', don't sell it if you don't plan to use it. Instead, find an arcane enchanter table and disenchant the object. This will let you learn its effects and apply it to standard weapons (providing you have a filled soul gem). The benefit here is that your enchanting will level up rapidly and you can sell the magic items for a pretty penny.