Remember that I will upgrade the gear if you think it is necessary and I agree. :)
Armor: Solid Cobalt , Magic Cloak, Jelly Mail (3)
Shield: Solid Cobalt
Helm: Elemental Hood
Swords: Silent Nightblade, Blazebrand, Blizbrand, Ascended Calibur (UV not important). <--4 star , Arc Razor 3 star...waste of 200ce...
Handguns: Voltech Alchmer2 in the making, Shadowtech alchmer mk2, and strike needle (not useful against jellies)
I have 3 weapons slots, do I need another?
Offhand, I'd say you honestly don't even need the third wep slot. I've never used it, but I do see how it can be useful. so...
I'd say go with silent nightblade, ascended calibur, and voltech.
That covers the weaknesses/resistences you'll face, plus the only thing you'll find elemental damage for (on jelly runs) are gun puppies and lumbers... both of which I prefer gunning. The nightblade is a must no matter what, since slimes are weak to shadow.
On that note you might ask about the shadowtech alch... I'd say your better off fighting slimes with swords, especially in the mass mob of the JK palace