Normal damage is great and all, but it's REALLY advised to get one weapon for each type.

Winmillion, I heard, is really fun, and since you won't have a gun (er, is this correct?), that's a wonderful supplement for ranged. Plus it fills the Normal catagory. Be advised that you'll need another weapon to go along with it, though, since you need a 5* weapon to pass the requirements.

Calibur is a really good as a bomb replacement, since it's charge attack is good for moving foes away, and it hits thrice. It deals pretty good damage, too, but it's a little lacking, since it's simple.

I've had both Cutters, and I must say, I was very disappointment. Just... don't. Sometimes the game can't handle button mashing, and you'll CONSTANTLY start charging instead of attacking during lag. DPS is lacking, considering it's speed, and the constant stepping of attacks sometimes doesn't catch up, making you whiff multiple hits. That basically means the only time it's good is when you abuse AI/shove enemies into a corner, and that's not fun, and only works on a singular foe. Also, low poise break, so expect yourself constantly getting greedy with hits and trading blows and OH GOD I DIED AGAIN CURSE YOU CHROMALISK.

But here's what I request: get a single type specific weapon for each type. You will not have a fun time constantly smacking guys with the same repetitive attacks, so for the game's and your personal enjoyment's sake, do this. I REALLY recommend:
Shadow: Acheron. Basically the highest possible DPS for a Sword, a true powerhouse with a simple, versatile attack. ...no, seriously, it's stupidly stronk, the fast attack also is an antithesis against the Shadow-weak enemies (fast gremlins and predictable moving jellehz), and it's strong enough to work even against ineffective foes.
Elemental: Avenger. It's a slow, wide, above-average length sword that will really complement your quick Acheron. It's got nice knockback, and has a projectile attack (or triple for Divine Avenger) and is still nice. I don't necessarily recommend you needing to take it to 5*, since you got Acheron to fill that requirement, but DA's charge is nifty enough to warrant consideration.
Pierce: Whatever. Yeah. Pick whatever you want. Most of these swords are all pretty good (heck, even the Status Flourishes, if you're smart with 'em) and are quick. For convince, I'd say the regular 'ol Flourish is great. It's charge is slightly better than the Barbarous Thorn Blade, but BTB is a brag trophy, if anything. And since you can get the Flourish recipe anywhere, it's cheapest.

As for armor and shield, you WILL need a 5* shield to continue, so you might as well get Swiftstrike anyway. It's wonderful for any situation, and my suggested weapons synergize crazily with that Attack Speed Increase. But yeah, go nuts with BTS. I personally never noticed any change in my shield's health between this and others. In post-game, though, my absolute favorite shield is Crest of Almire. It's has awesome normal defense, and since there's PLENTY of Shadow damage-rs, it's wonderful for them. And did I mention FFIIRREE AANNDD SSHHOOCCKK DDEEFFEENNSSEE?? Seriously get it.
For armor..... uhhhhhhh.... I guess not Chaos. Chaos is absolutely broken for any build, and devastates most floors with those crazy attack buffs, but consider more defense. The Wolver paths are pretty great, but keep in mind that you'll look like a nublet if you choose Vog Cub. It's basically the Giant Dad of this game. And... Snarb is pretty good. You'll need alot of help getting someone to take you, but it's really great, and you'll look sexy with that boss armor.

Pick your poison, punk. :^)