The STR and Attack one is fire path, which is virtually impossible to do. I'd not recommend it because honestly, you could get an Almace or the WoE equivalent upgraded for much less work than the fire Shamshir. And an Almace is superior to a fire Shamshir.
I did the ice ones myself, because ice is the easiest path and the damage/delay ratio is good. Also, +20 INT/+20 MAB is pretty nice for Sanguine Blade, which will outdamage every other sword WS short of the empyrean if you build for it.
Wind/Earth would likely see more use if you like to solo or tank a lot, Fire/Lightning are better for meleeing, but honestly if you want the best melee DPS swords, Almace or the WoE variant and the DA+10% Khanda are your best bet.
I don't think Dark, Water, or Light are particularly useful.
I'd do either Ice, Wind, or Earth myself. Fire is 'better'(tm) but not worth the effort, as superior weapons are easier to get. Ice (mab) is easy and can be done in an afternoon. Wind or Earth (Eva or -PDT) take longer, but will remain eternally useful for their niche applications. Lightning is handy if your acc is bad for some reason, but I'm not sure you'd ever take off your Almace or Khanda for it, so unless it's one of the easy trials...