1. Make sure you have at least one weapon type as a major skill. Few things are more frustrating in the game than missing 9 out of every 10 swings.
2. Keep an eye on your Fatigue. It affects all sorts of things, from how effectively you fight to how successful you are at casting spells. Above all, NEVER enter combat with a drained Fatigue bar, as enemies will knock you off your feet and wail on you mercilessly.
3. If you're uncertain of your combat skills, stick around the Bitter Coast region for a bit. There's plenty of easy mudcrabs, kwama cuttle, rats and slaughterfish to kill.
4. Make sure you have at least one silver/enchanted weapon with you (preferably a weapon type you're skilled in) if you plan on raiding tombs or Daedric ruins.
5. Keep your weapons and armor well-maintained. If you made Armorer a major or minor skill, I recommend you repair your own gear. Otherwise it's more cost-effective to have a blacksmith do it for you.
6. Keep an eye open for airborne attacks, particularly when you head inland. Cliff Racers are freaking everywhere (on the plus side, you can sell their plumes for a pretty penny).
7. It's not a bad idea to invest in the Alchemy skill. It allows you to make useful potions out of all sorts of common ingredients (you can also sell your concoctions for extra money).
8. Don't go too crazy harvesting any plants you come across. It takes a full month (game time) for them to grow back.
