The Calibur series is pretty good, with a useful charged attack. With other swords you have to worry about enemy resistances-- the Flourish series won't hurt Constructs or Slimes at all, and the Brandish gives you a different blind spot with each of its different upgrade series. The Spur's upgrades make auto-dodging enemies sidestep or block your attacks, and the Cutter line puts too much emphasis on attack speed rather than making the enemy stagger or knocking them back.

Calibur is very useful in almost all situations. Except the situations where you wouldn't want to use a sword. But the other swords have the same problems anyway.

Swordstones are dropped by mechs mostly. Robo arenas are good sources.
However, given the prices in the auction house... You can simply buy a brandish or calibur for 1500 or less. You can buy one with a low unique variant - at least bonus damages - for less than the cost to craft one. At least today, who knows about tomorrow. If I was starting today, I'd grab a calibur with bonus damage vs something, or if I was really forward thinking and patient enough to save more money, attack speed increased.

Swordstones are dropped by Mecha Knights and Retrodes (humanoid robots with three eyes that move slowly and claw at you or shoot lasers in later tiers). Some Gremlins also have them.

Note that it's a 2-star material, so it only drops in Stratum 2 and deeper. That means Depth 5 and onward. If you're still in Tier 1, look for Gates that have a construct- or gremlin-themed stage in the second half (that is, after Basil and the Clockwork Terminal). All arenas, regardless of elemental and monster type, will have a number of Mecha Knights as "generic" enemies. (Plus they're pretty worthwhile in general if you can handle them.)

Oh. Other new equipment...

The Wolver set has not-so-useful Piercing defense, but also offers pretty-darn-useful bonus damage when you attack with swords. You can wreck stuff a good bit more quickly with Wolver on. If you're more concerned with your defenses, you can try out the Magic Cloak-- Normal and Elemental damage are the two most common types (though you might look silly until you have both the cloak and the hood together). For your shield, you can go with the Plate Shield series (Gobs and gobs of Normal defense, can take a good amount of hits, and is heavy enough to push larger monsters) or the Owlite Shield series (Useful status resistances and it can stand up to Elemental hits).

Normal is the most important defense;
Elemental is second-most important;
Shadow is in third place;
Piercing is only present on spike traps and Lichen Colonies, both of which are predictable.

Start learning to shield properly. It's a necessity in tier 2 and 3. If you don't, you'll just keep dying and that won't make your fellow party members very happy.

If you do not know how to use your shield well, you will be mauled horribly in later tiers. Most enemies will no longer flinch when attacked, and many are simply designed with the expectation that you block and then counter (Greaver, Gun Puppy). The red health capsules are too precious to waste. A dead player cannot kill anything.

First, know that you can "Shield Cancel." If you press and hold your shield key mid-combo, your guy will start shielding more quickly than if you had waited for your sword swing to end ("canceling" the downtime animation after the attack). This works on any swing that's not a combo finisher-- so sometimes it's worth just swinging twice and then shielding rather than following through the full combo. When you see an enemy's attack-warning-lights, shield-cancel out of your combo and block it.

Second, and also very important, is the "Shield Shove." (Also known as "Shield Bounce" and "Shield Bash.") If you press your shield button when there's one or more monsters right up in your face inside the shield bubble's range, the monsters will all be pushed away from you a certain distance. (The push force varies from shield to shield-- bigger shields tend to have more shoving force). Due to latency, this happens a split second after your shield appears to actually come up-- so time your shove accordingly. You can only shield-shove once every few seconds-- you can still block, but enemies won't be shoved away if you try to shield again before that. You'll know if you successfully shield-shoved someone if you see a burst of sparks pop out and surround you. (Though it might not do anything if the enemy's too heavy for your shield to shove-- like trying to push a Lumber Golem with your Proto Shield. In that case the shove was wasted but hopefully you at least blocked an attack with it.)

Set your Defend key to something in easy reach. I use WASD for movement, so I set my Defend button to Left Shift. It's almost as important as your weapon.