I like to stick to the main quest until I receive the final word of Unrelenting Force (Fus Ro Dah), then I'll work on some side quests, usually starting with the Companions in Whiterun. Eorlund Graymane will hook you up with a Skyforge Steel weapon of your choice. Another option is to race through the main quest until you learn Dragonrend, as that will make the whole dragon killing thing a lot easier.
Misc tips off the top of my head:
Pick up/buy all iron ore/ingots you can and craft iron daggers to get your smithing skill up. Use any gold/silver/gems you find in dungeons to craft fancy jewelry as well, as they'll level up your smithing even faster.
Work on enchanting as well, find/enchant a weapon of soul snares to constantly fill your empty soul gems, and use the gems to enchant the daggers/jewelery and then sell them. Keep an eye out for an item with the 'Banish' enchant, once you can craft a weapon(hundreds of iron daggers that is) with that particular enchantment, you'll never have gold problems again.
Archery is also a very useful skill to have leveled up, have Faendahl in Riverwood as a companion and have him train you in Archery 5 times, and take your gold back from his inventory. You can do this again if your character levels up (5 training sessions per clvl) up to 50 archery, which is an excellent start.
Once you have your gold situation figured out, it's good to buy/pick up every ingredient you see, stuff em in a chest in your house (probably Breezehome in Whiterun) and eventually go on a potion-making frenzy, then sell them all. (Potions are excellent gold:weight ratio)
Don't be afraid to adjust the difficulty, you'll technically level up faster on higher difficulty by taking/dealing more damage overall, but sometimes those pesky high level mages and the like can one-shot you on higher difficulties like Master and Legendary.
Use the Lovers' Stone (East of Markarth I believe), it grants you a 15% exp bonus for all skills, as compared to a 20% bonus for one of three groups of skills from the Mage Stone, Warrior Stone, or the Thief Stone.