Firstly: in the long run, you're going to be leveling a lot of different jobs. First to get to level 18, where you can get a subjob, which you will also have to level. Then, once you get to level 30, you can begin gaining access to all of the additional jobs. Different jobs and different situations require different subjobs, so even for a given job, you will want access to three or more different subs.
Second: realistically, you are going to spend a lot of your early career leveling solo (with Trust NPCs to support you).
My personal suggestion is to start as a warrior. It is a relatively easy and straightforward job. While it is not in high demand as a main job later on, pretty much every melee job will want it as an option as a sub job. In addition, as you are leveling early on with trusts, it is a slight benefit to be able to remain engaged and possibly taking hits as warrior.
Once you get warrior to 18 or higher, you can unlock the ability to use a sub job. At this point, you could level something else with warrior as a sub, or begin leveling some other subs, and take warrior up to 49, to have available as a sub for future lvl 99 jobs--you are almost certainly going to want warrior to 49 or higher for any melee job.
Alternatively, if you want to play a mage, you could do the above with red mage (slightly better armor and weapons than other mages) and take that to 18 or 49 as support for future mage jobs.
As Nanako said, you're going to want a job with sneak and invisible spells or abilities--that is white mage, red mage, scholar, dancer or ninja. Scholar, dancer and ninja are unlocked after level 30, and may require some sneak and invisible to access on their own.
Good luck, and happy adventuring.
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Renatus (Titan)
"We are Dragoons, and to make short work of foppish cavalry is our bread and butter."
-Bob Shaftoe, The System of the World