To many people, equipment at earlier levels simply consists of getting the most attack on everything. That doesn't always work, nor is it the best thing to do if you want to train quickly. Because I'm having trouble formatting this section, new players (whether this is your first character or first warrior) will need to read through this entire section from top to bottom. I can't find a way to put it neatly without confusing everyone, so I'll lay it out in order of level ranges.
Level 10-19
You are a swordsman, but that does not mean you need to use a sword. Use whatever you can find and equip, don't bother buying anything (you probably won't have the money for it either, and you need to save up). The same goes for armour - you don't need it because it's not going to help much, if at all. The defence you gain from armour is not significant in any way.
- The Andras Hat can be obtained from a quest once you reach level 18. It adds 12 STR, which is quite a large bonus. Chances are you will be using this until third job.
- Blue Ribbon Pig familiars (level 13) give 8 speed and jump while you're on Victoria Island. Granted you won't be leaving so soon, use it for the speed.
- Jr Boogie 1 familiars heal 15% mp every 10 seconds. While that isn't a lot now, just get three cards. Use them when you get the speed to replace the Blue Ribbon Pig familiar.
Level 20-29
- Bathrobe, which gives 10 ten speed. To get it, you need about 31k mesos. If you have to, start selling your HP potions or something. This is an incredibly useful piece of armour, one which I recommend you use until level 90 or so (seriously)
It doesn't need to be scrolled for anything. The main thing about it is the speed bonus - speed allows you to reach the next monster quickly, and travel quickly.
- Whitebottoms, which add 3 speed. These can be bought in Henesys, or gained via a quest in Kerning. Although 3 speed may seem quite useless (it is), these shoes can be scrolled for speed. To buy these scrolls, you'd need to find the scroll sellers in Orbis/El Nath, Ludibrium or Leafre and have 175k. If you don't have the mesos for it, don't bother.
Level 30-39
Again, there isn't much here.
- At this point, you will start adding Mastery and Booster. For Pages, these skills only work on Swords and Blunt Weapons, so logically you'll be choosing one of those. Again, choose whichever makes you kill mobs in the least amount of hits.
- Mushking Gloves are an option, adding 1 attack. That's not a large bonus, but you may as well.
- The Mushroom Kingdom medal gives one to all stats, as well as 100 HP and MP. In my opinion, the most useful thing is the MP.
- Although this is really equipment, you can now choose professions in Ardentmill. I strongly suggest Accessory Crafting or Alchemy (or both, if you have the characters and money). Both are extremely useful in their own way.
Level 40-49
- Get a new weapon, either by finding it or through Monster Carnival.
- If you can be bothered, get the Free Spirit Piercing (earrings) from Kerning Square Mall by completing the quests. They're not necessary in any way.
- If possible, the Icarus Cape (2), which adds another 10 speed. You might get it, you might not. Don't freak out.
- The One Who Touched The Sky medal, which adds 5 speed and 5 jump.
- Squishy Shoes or Soft Jelly Shoes from Kerning PQ. It may be hard to find people, so don't waste your time if there's no one there.
Level 50-59
- If you feel that it is really necessary or just want to waste your money, you can get a Zakum Helmet. But I think that you could live without this, since you're only gaining about 7 extra STR (3 STR and 15 DEX) for...a lot of money.
- The Japanese Map, if you can get your hands on it, is an extremely powerful weapon. It has the strength of a normal two-handed sword, but is faster than most one-handed swords. With booster, you will hit the speed cap. You can use this weapon all the way until 90 or 100 if you can find it. Finding it is the main problem.
Level 60-69
- Although it can be obtained earlier, the Broken Glasses from completing Ludibrium PQ 35 times are useful, and you'll probably have finished 35 PQs by this time.
- Nimble Ring I. This gives you 5 speed, and can be made via Accessory Crafting (or just find an Accessory crafter and ask them to make it for you). You can only equip one at a time.
- The Chryse Medal, if you have the patience for it.
Level 70
- Nimble Ring II. You can equip both Nimble Rings if you want, because they are different.
As you can see, most of this revolves around gaining speed. Explorer warriors (only explorer warriors, it seems) lack mobility in any form until fourth job, so you need to get it yourself. Speed is more important than jump, and also much easier to get. It gets you to the next mob faster, and allows you to sweep maps at a faster rate. Attack and extra stats will also make you train faster, but speed is the easiest to get, especially for new players. Older/richer players should be able to get both speed and attack - attack being only a matter of a better weapon and possibly a scrolled work glove.