Alright, so I've done some investigating and some translating to get some more information from the modes trailer, particularly about the two screenshots from the museum for the weapons, to see if they put any hints in there. I've gathered that it does appear that each character is going to be getting 7 weapons, that joke weapons don't appear to be a thing (or if they are, then they're not in the museum, but that doesn't make any sense, because joke weapons were in the museum in prior games), and also that not every character is going to get a Soul Edge, so the theory that everyone's seventh weapon is going to be Soul Edge for Inferno to use as a mimic is also out the window. So it just happens to be that Ivy is apparently getting Soul Edge for the first time, not counting Soul Edge (Complete) from SoulCalibur II, because everyone got one of those. Another thing of note is that it also doesn't appear that 2P weapons for everyone is going to be a thing, since none of the folks in the museum seem to have them.
So, starting us off with the first screenshot, we're in Xianghua's territory. We don't see her first weapon (even though, without a doubt, it's Krita-Yuga), but we do see her other six weapons, as follows:
Qing Long
Makhaira
Kard
Northern Star
Straight Sword
Soul Calibur
Pretty standard fare for Xianghua, really, though she is inheriting Makhaira from Leixia. There is a potential (!) red flag here, in that she also has QIng Long, which was Leixia's curved sword stand-in for lack of a Korean swordsman in SoulCalibur V. That being said, Xianghua did have this weapon in SoulCalibur II, but it went by a different name, Qi Xing Sword, so I wouldn't take it, in and of itself, as a deconfirmation of Hwang. Though it is notable that Xianghua did not have it in SoulCalibur III or SoulCalibur IV, as Hwang had it in SoulCalibur III and Yun-seong had it in SoulCalibur IV, so it's... let's just call it a 50/50. There's still plenty of curved swords to go around, after all.
Next up is Yoshimitsu! Let's see what he has in store:
Manji Sword & Fu-ma Blade
菩提 (Bodhi? As in Bodhisattva? New weapon?)
Kagekiyo
Phantom Machete
Chevalier
Wooden Swords
Hihiirokane
It's mostly, pretty much, almost exactly his weapon loadout from SoulCalibur V, with the addition of his classic ultimate weapon, Hihiirokane, which will for sure be nice to see again in all its crimson glory. I'm pretty sure my translation here is accurate, and I'll go ahead and address the weird elephant in the room... it actually appears that Yoshimitsu, the man whose name is supposed to be earned by his possession of the sword, Yoshimitsu, does not actually, in fact, use the sword Yoshimitsu! I'm personally chalking this up to the fact that in the story, Voldo steals Yoshimitsu from Yoshimitsu, and so, in the meanwhile, he's using Manji Sword as a temporary stand-in. It's just kinda weird that none of his other weapons are Yoshimitsu, either, for when he reclaims it. I'm really not sure about the second weapon, either, as he's never had a weapon by this name.
And, lastly, the highlighted weapon on the page is... Nightmare's Soul Edge. Nothing really special to say here, kind of a shame we can't see what other fun weapons that NIghtmare will be able to wield in this game. Oh well. On to page two!
This time, we're looking at Mitsurugi's exotic blades. Again, his first weapon is missing, like Xianghua's, but we can practically guarantee that it's Shishi-oh. What about the rest? Let's see:
Damascus Sword
Tyrfing
Hide in Shadow
Two-Handed Sword
Kokuenra
Masamune
I guess Tyrfing wasn't good enough, because we also have the classic European-style sword again, the Two-Handed Sword! I'm actually really happy about this, since I vastly prefer its design over Tyrfing. The others are pretty much staples for Mitsurugi, and it's nice to see that he got the real Masamune back this time. It's nice to see Kokuenra making a return as well.
Moving on, the next in line is none other than Seong Mi-na! Who has a couple oddities in her list:
Scarlet Thunder
翠雲 (Green/Jade/Emerald Cloud? New weapon?)
Ambassador
Halberd
Hraesvelgr
Hyup Do
太古の槍 (Ancient Spear/Lance? New weapon?)
I'm not sure if it's just the blur, my awful vision, my rudimentary ability to decipher kanji, or somewhere inbetween, but I just have no idea what the second one is supposed to be. Not even a little bit of a clue. The obvious choice would be Defender, but that would be written in katakana, so that's not it. The rest of her weapons are basically exactly what she had in SoulCalibur III and SoulCalibur IV,
and the last one, I'm not for sure. It's Ancient... something! Again, I just can't decipher the last kanji, so maybe someone more skilled than I can figure it out. But I really have no idea what it could be, perhaps another new weapon like Yoshimitsu's Bodhi(sattva)? Last weird thing is that Hyup Do (pictured) really seems out of place, since it's usually lower in the chain. Hraesvelgr is somewhat her ultimate weapon, even! I wonder what's up with the ordering.
And last, but not least, but also not very exciting, we have Taki's Rekki-Maru & Mekki-Maru. Nothing else really to say about them.
Edit: Added translation for Mi-na's last weapon, thanks to @Ninjaguy446 for the assistance!
Edit 2: Added translation for Mi-na's second weapon, thanks again to @Ninjaguy446 for having sharp eyes!