All this information is relevant to main story progression; the rules change (somewhat) at 50


1. Ask yourself, "is it the right kind of gear for my class?" A lot of early gear isn't class-tied (especially accessories), but it may not be appropriate. For you as an Arcanist, make sure you're wearing +Intelligence as much as possible. Even if something were to have, say, +10 Strength compared to your current +5 Intelligence piece, that piece of Strength gear would be funcitionally near-useless to you and not worth it. Note that +Vitality is on almost all 'left side' gear for free; but accessories will be one or the other, and +Vitality accessories are meant for tanks.

2. Better item level generally = better gear. While you're levelling, item level is about the same as the equip requirement level. That said, items while levelling tend to fall into three tiers:
-Standard gear (white, normal quality) is the 'baseline' power for a given equipment level.
-Aetherial gear (pink dungeon drops) are slightly enhanced thanks to extra random substats, and slightly better than normal quality.
-Green gear (dungeon drops) and High Quality white gear (made by crafters and often sold on the market board) is much higher than normal. Consider this gear to be 3-4 levels above the minimum to equip it, because that's effectively what it is.
If you're uncertain, compare numbers like the Weapon Damage (on weapons), defensive stats (on left side pieces), or just raw +Intelligence (on right side pieces) to determine which are more powerful.

3. Not all equipment is an equal part of your power. In order from most important slots to keep upgrade to least...
-Weapon is not just the hugest chunk of your stats, the weapon/magic damage is used in almost every numerical calculation you output (Damage, threat, healing...).
-Next, Shirt and Pants have the most stats attached, especially defensively
-Head, Hands, and Feet have significant stats attached as well, but less than the above three
-Waist has less stats than other left side pieces but still affects survival as well as core stats
-Accessories (all right side pieces) have no defensive stats attached but can still amplify Intelligence (or your other primary damage stat). Accessories are harder to find upgrades for though; generally you'll only get them as occasional quest rewards, dungeon drops, or on the market board - after about level 25-ish you won't find them sold by NPCs.

4. As for keeping things updated? Your weapon should ideally be within 5 levels of you. The remainder of your gear is sufficient at about a 10 level gap, but don't wait forever to upgrade; the more you keep your gear updated the better.

5. Gear that uses multiple slots can be confusing, as it has the stats of multiple slots. A cowl (shirt + head) that's level 30 will probably appear stronger than a level 35 shirt... but that level 35 shirt plus a level 35 headgear will be stronger.

6. Looking for gear? Follow your story! The storyline will take you to various locations, and those locations will have vendors selling standard quality, level relevant stuff (EG the story at level 30 will take you straight to areas with NPC vendors selling level 30 gear). It won't be as good as crafted or dungeon drop gear, but this is a great way to replace slots which are starting to become outdated. You also get lots of free equipment from sidequests, too!

7. Finally, if you really want to farm for gear, the best gear available to you will be in whatever the most level relevant dungeon is to you. Which is also where you'll get the best EXP for your time, so hey!