What's the most fun tradeskill?
Depends how you define fun. Cooking I would say is the hardest to level (at least later on) purely because most of the ingredients are dropped by mobs or harvested. All the other ones are pretty much using materials you get from botany and mining.
Depends also what you want to get out of the trade skill. When I first started, I went carpentry and botanist, because I figured I could harvest lumber and then make stuff. However, I quickly learned there is a lot of tradeskill inter-dependency. Like I need hinges to make something, but hinges are made by armorer. However, you can level ALL the tradeskills on a single character.
This is what I would recommend:
1) unlock all the tradeskills - if you do the noob quests, they give you a fuckton of elemental shards that you need to craft with. Even if you dont plan to level one right away, the shards might be used by another tradeskill (for instance, cooking and blacksmith both use fire).
2) You can pretty much level all the way to 10 by using vendor bought shit on most trade skills. The trade guild will have some of the noob materials, if you have a FC house with a materials vendor, they sell slightly more leveled stuff also that can be used
3) When you hit level 20 or so, start to use tradeskill leves. They're basically repeatable handin "quests" that give you a set amount of XP for either a normal or high-quality handin. Your character gains a few leve allowances every 8 hours or something. They are extremely helpful and can get you a fuckton more XP than just straight up grinding
4) Level gathering - botany and mining mostly (fishing is really only used by culinarian, with a couple exceptions). Gathering your own materials helps you level crafting for much less. There are also gathering leves you can use to level
5) tradeskills use your rested XP bar - keep this in mind. There isnt a distinction between rested XP for combat or crafting/gathering
6) When you unlock HW, you can eventually unlock the Firmament. It makes power leveling crafting classes pretty easy. So if you later decide to become an omnicrafter, that can help.
7) There are beast tribes devoted to crafting. They give you crafting XP for daily quests. ARR = Ixtal, HW = Moogles, SB = Namazu, ShB = Dwarves. Ixtal are a pain in the ass though and the XP isnt that hot. You're better off just trying to get crafter to 50 so you can use moogle beast tribe after you unlock in HW, which gives much better XP.
8) To save money, try to keep your tradeskills in rough proximity with eachother level wise.