I used to play Skyrim extensively, but now I've calmed down on it. Some advice:
When looting, try to go for the high value, low weight stuff first. There will be times when your carrying capacity is approaching maximum weight allowed, and you'll need to make choices in what you take with you. Unless they place is particularly far away, you can eventually go back with fast travel.
Focus on a "craft" skill (alchemy, blacksmithing) as a way to make money. You can create superior equipment this way, and sell stuff you make. Enchanting is cool as well for putting magic enhancements on your armor.
For the dragon fights, you'll need a good ranged attack. Whether it's arrows or spells matters little as long as you're good at it. A pure melee character is not going to have fun fighting dragons. Train yourself in destruction magic/archery for this.