I would recommend starting with Mining/Botanist before diving into crafting. This will let you gather the items you need for synthesis, saving you money in the long run.

I would also recommend leveling all the crafts to 15 first, then pick the ones with 50 skills you need and get them there before moving onto the next ones. I'm not a fan of leveling all the classes equaly after 15 because you can dump all your leve allocations into one class, getting it to 50 and it's 50 cross-class skill faster.

Blacksmith and Goldsmith are good to level early since they make a lot of gear all your other classes will use. Alchemist and Culinarian have some of the best cross skills, but they are hard to level because you can't make their material with other classes like you can with Blacksmithing and Armorsmithing for example.