All the crafting classes learn and use the same abilities now so it's less which is easiest and more which is most useful to you if you only want to level one. There are advantages to leveling them all since they're mostly interdependent for materials (CUL being the odd man out) plus having the correct class leveled allows you to repair your own gear.

GSM tends to be a common pick for those starting with just one since it makes most right side accessories, allowing you to repair about half your gear.

The first time you craft a recipe, you'll gain an XP bonus on top of the normal XP for completing the recipe so it's good to make different items for that bonus if you're not using leves or collectables for XP.

Don't neglect doing the class quests when available. Each is worth almost a full level of XP if done at the appropriate level and will need to be completed to unlock an important ability at level 65 (Manipulation).

There are vendors scattered around that will sell most (though not all) materials needed for leveling up to 70 if you're not gathering them yourself. Keep in mind prices can be better on the marketboard for many of the materials. You can check the material tooltips for the vendor prices to compare if you're looking at the marketboard prices. If (Restricted) appears after the price, it's sold by one of the beast tribe vendors that requires a quest unlock and sometimes a reputation standing.

Try to at least keep your tools up to date while leveling if not also the rest of your crafting gear. They're going to give you the largest percentage of your craftmanship/control stats that you need. CP also becomes very important once you get past level 50.