When should I start worrying about gear?

[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.