Okay, cool. If you're using a Physical-based Longsword, I believe you already get the Iron Knuckle from that branch which buffs physical attack. I also recommend Supreme Sword from Blast Fencer (massively buffs melee arts used one after the other in quick succession) and Mighty Muscle from Striker which you should also have already (flat melee damage increase).
If you use an Ether-based Longsword (like most Longsword people do at endgame because Ether skills + the Blossom Dance Art you get later is mega OP), you'll want Core Crusher from Psycorrupter (makes you unable to break appendages but buffs all Ether attacks by 150%), and Ether Boost from Blast Fencer (flat ether damage buff). Similarly, with Electric-based weapons you want Electric Boost from Partisan Eagle (flat electric damage buff), Conductive Strike from Astral Defender (300% damage buff on enemies inflicted with Shock). For Beam-based weapons you want Beam Boost from Blast Fencer (flat beam damage boost).
For weapon augments, Weapon Attack Plus is good but hard to come by. Melee Attack Plus is much easier to come by and will work well early on. For Ether, Beam or Electric builds you want that element's attack up as they are higher return than the Melee Attack Plus and better than most of the lowbie Weapon Attack Plus buffs (the high end versions are better though). You also want that element's Nullify Reflect augment to ensure nothing can bounce your attack back at you, and in the case of Electric you also want Melee: Shock to inflict Shock with melee attacks, activating the huge boost of Conductive Strike.
With that general stuff you should be able to figure out what works for your build and see an increase on your damage. Half the time I don't even use Skells because I can take something down much faster on foot.
