I would generaly focus on leveling multiple crafters at once. Mainly because they synergize a lot and can make the later levels a lot easier. And while it might look like its slower, if eventualy going for all of them, this is significantly faster.

Culinarian is an exception as it doesnt rely on the other crafting classes, and instead relies mostly on gatherers, but culinarian often requires a lot of ingredients compared to the other crafters, and is also generaly a lot more difficult to sell items with (a lot of people do not care about food). I would not recommend this.

For other classes, if taking only one, you generaly will notice that around lvl 35 it will start to become anoying to obtain the items (the nearby stores no longer sell the items you need), unless you just resolve to the market for buying. Especialy at lower levels, most of the items are relatively cheap (gathering yourself is however still better, but if you have plenty of money, it might be a timewaste you dont want). Beyond lvl 50 you are going to rely on a lot of other crafters, or end up overpaying a lot on the market.

To decide your class (or classes) it is best to look at crafting jobs that are close together to make it easier to level multiple jobs at once. For example:
- Smithing/Armorer
- Leatherworker/Carpenter
- Goldsmith/Weaver/Alchemist

These are all either close together, or within the same region making traveltime towards each other short. You can often combine the quests of these and speed up their leveling.

For these classes it also depends a lot on which gatherer classes you have. As for example carpenting synergizes well with a botanist while smithing goes well with a miner. This can make it easier to reach lvl 50 with those because you can often gather a big bulk of items (including shards). Beyond level 60 all of them are somewhat similar though as they have a lot of ingredients that are produced by others.

In the end, it realy depends on the type of items you focus on most, and what you prefer to level yourself, as all of them are somewhat similar in speed to level. And quest wise all of them are similar in difficulty regarding the items to obtain and things to craft.

Another important aspect is to make use of the daily deliveries of the grand company. This is generaly the fastest way to level for the effort you use. Each of them give a lot of XP, and can grant up to 4 levels for a single item (if its starred and HQ) when below lvl 50! For this alone i would suggest unlocking all crafters, even if you just focus on 2 or 3 of them. Just checking the market for potential items you can turn in can do a lot. Some of those starred items are sold on the market for 2k in HQ, which is a lot of fast levels!