The crafting classes are interconnected enough (both by cross-class skills and by using materials made by the other classes) that people who get heavily into crafting usually do all of them. If it's too daunting to work on all eight at once, though, pick a couple that complement each other well and focus on those for a while, then later go back and pick up a couple others. Use the levels important skills come in as milestones, so you might start with a couple classes, take them up to 15, then pick up a couple more and do the same. Once all are at level 15, go back and take the first ones up a few more levels, and so on.

Weaver and Leatherworker, for instance, seem to work well together, since many WVR recipes need some leather and some LTW recipes need some cloth. They also make a lot of the crafting gear if you want to equip yourself, so that could be a good starting point. Picking up Goldsmith for jewelry and Blacksmith for tools would get you the rest of your crafting gear. Culinarian and Alchemist are the least interconnected with the other crafting classes in terms of materials needed, but are highly dependent on gathering classes (especially Botanist).

Just as with the combat classes, the early few levels are fairly quick and easy, so that you can learn along the way.