First of all, always remember to use the offline training statues (or bed in your house) when you logoff. That's a premium only feature that will speed up your skilling process by a ton in the early stages of the game.
Then, your question is somewhat open-ended, given the nature of the game. The most basic thing you can do is level your character in premium areas, since level matters a lot when it comes to enjoying other aspects of the game, such as bosses and quests. Since you're starting a new character, try to choose a premium city when leaving Dawnport, and start your adventure there. Kill monsters for xp, and when you feel like in need of a change, there are several long quests that you can experience only as a premium, like Explorer Society, In Service of Yalahar, New Frontier, Inquisition, Secret Service, which are most overlook nowadays by old players, but might interest a new premium player like you, since they open up new areas or gives access to items and useful mechanics.