Preferably leader with respect and love for his/her family, or just being understanding, so that it wouldn't be a repeat of my old shell. "Tell your family to gtfo and slam the door!" "If you can be online at all, you have to come to event." etc. That I'm online doesn't always mean that I don't have to constantly afk to reply to something someone yelled from other room or enjoy a moment of chat and icecream or hot chocolate. I try my very best to, but if the situation is so that out of 24 hours in the day, there's only 3 that there could be family time, and those three coincide with Dynamis, I will choose to be available to them. (that's assuming that didn't go out in the first place if it's evening) And no, I can't know for sure when those hours will be, it's random when people will come home.
And personally I think it's more harm than good to have someone repeatedly afk in Dynamis for unknown periods of time, in that case it'd be better not to come at all. I don't cherry-pick that I only want that area... and that area... and that area, I don't even look what Dyna there is before I know if I can go.
I understand that in that case I'd be lowest of the low on the list of drops, and I'd never bitch as long as I was over "everyone pass so that it disappears in the abyss" tier. ^_^
Best times would be any time between 8 am and 6 pm GMT+2 (10 pm and 8 am PST) during week, earlier or later than that is more likely to coincide with family time (or I'm sleeping :P). Or between 6 pm and 10 pm on weekends, because weekends are negotiable that we'll do this and this during day, and then I'll get me time on evening, ok?
Some of the weekdays could be shot on autumn once active classes start (summer time is mostly IRC meetings and home studying), but I have quite big freedom to plan my days, so I'd try to work around Dyna times if they're on weekdays.