You can solo all the way to level 60 with any class. Or you can group at really any level. You'll need to group to do elite quests most of the time, and dungeon quests.. but regular quests can all be done solo.
Grouping and going into instances is the best way to get loot as you level. And when you log out you'll want to sit your character in an inn or inside a major city so you will get rested exp while you're offline to help you level faster.
