When should I start worrying about gear?

[lujate]

For example, my L10 Gladiator is still using the starter sword.

[jabbywocks]

You should be getting better armor and weapons if you're following the main story quests and also most side quests and class specific quests give equips.

[Asdamine]

Do not worry too much about it. You will get most of your gear from dungeons. No need to buy gear from the market or take the gear from quests (always take the coins, because those gear are cheaper than the coins you get from those quests).

Update your gear as you get gear from each level of dungeons, starting from lv15.

At level 50, that's the only time you will majorly spend your money on gear to update every weapon(s), accessories, belt etc to lv50 to prepare yourself from en-game dungeons farm.

[Niwashi]

For example, my L10 Gladiator is still using the starter sword.

That sounds like you missed the class quests, as those will give you a new sword each five levels. Remember to do your class quests every five levels on each class, as not only will they keep you reasonably up-to-date on weapons/tools while leveling, but that's where you get some important class skills as well.

As for armour upgrades, as Urthdigger said, about every five levels or so. Less often (maybe 10 or 15 levels) for jewelry. For your first class, quest rewards will keep you reasonably well geared, but you may need to purchase or make gear for later classes.

No need to buy gear from the market or take the gear from quests (always take the coins, because those gear are cheaper than the coins you get from those quests).

Actually, in most cases the coins are worth significantly less than the NPC vendor price of the equipment. I usually check the market boards to see if there's a particularly cheap deal on the item in question (in which case I'll buy it there and then take the coins as a quest reward), but otherwise it's best to take the gear reward whenever it's better than what you currently have equipped.

[Lillia]

-snip- Actually, in most cases the coins are worth significantly less than the NPC vendor price of the equipment. I usually check the market boards to see if there's a particularly cheap deal on the item in question (in which case I'll buy it there and then take the coins as a quest reward), but otherwise it's best to take the gear reward whenever it's better than what you currently have equipped.

Well we'd also probably wanna keep in mind that prices varies between servers.

[AnimaAnimus]

Update your gear as you get gear from each level of dungeons, starting from lv15.

Horrible advice. You walk into a lvl 15 dungeon in lvl 1 gear I am out, idc how good you claim you are. You should always keep your gear upgraded. If nothing else it makes dungeons, fates and hunting log kills all the much faster. And the gear is so cheap and can so often be used cross-class there is no reason not to keep it up to date.

[JagerForrester]

The important thing you will be spending money on is transportation (chocobos, teleports, ferry rides, airship rides). You can get by with just getting gear from the story quests, class quests, and the miscellaneous quests along the way. This will take you all the way to 50. Keep the "Recommendations" window open to stay alert of any quests available to you in the vicinity.

[GinTama]

update your gear before going into a dungeon

[Toranja]

You start getting killed would be a good indicator.

[Urthdigger]

I'd say a good rule of thumb is to upgrade your gear every 5 levels. If you do your class quests, they will upgrade the weapon for you. While you CAN just use gear from dungeons, you're likely not going to do so well in the level 15 dungeons in level 1 gear. That argument also assumes you're regularly running dungeons. If you're running FATEs to level like 99.9% of the population, you're not getting gear as you level.

So, yeah. Upgrade every 5 levels or so.