My first week I just lotted on whichever Crimson piece came up first, which was the crimson tights after 3 or 4 runs.

My second week I was going for the vest, and over the course of about 10-15 runs it did not drop. I saw the crimson gloves early on, which I passed on, and eventually just lotted on the crimson boots since it was nearing the end of the week and I was getting tired of running it over and over.

My third week I went for the crimson vest again, and got it on my third run about 1.5 hours after the weekly reset.

I think the most common pieces I see are bard, although my first week it was more weighted to tank. Dragoon pieces come up fairly frequently for me as well. It doesn't seem overly unbalanced in terms of what drops to me, however. RNG is RNG.