Since Fevvers and Warm Mist brought up sakuga, I thought I should chip in a little too because this show has a lot of important names (in fact, almost one every episode) that nobody mentioned yet ...
The MADs in the spoilers contain spoilers to multiple other series, open at your own risk.
Episode 1 + ED
The person who did the Akki scene in episode one is Shingo Yamashita; he's also the one who did the entire ED by himself (which by the way is a very heartful and beautiful ED).
Episode 3
Arai Jun as mentioned is another talented animator; people should know him from Star Driver.
Episode 4
中瀬理香 ヤマトナオミチ
小倉陳利 近藤圭一 (Scriptwriter, Episode Director, Storyboard, Animation Director)
We don't have the actual gengashi list yet obviously, but from the staff list Ogura Nobutoshi is another guy to keep an eye out for.
Episode 5
浦沢広平
山内重保 山内重保 羽山淳一
Yamauchi Shigeyasu is an ancient giant who participated in many storyboard and directing. Hailing back to Saint Seiya days, most recent one I remember is Penguindrum episode 18. He worked with Hayama Junichi with the same episode there and IM@S 9, who is another veteran.
The list is probably not comprehensive, but as I've said previously I have huge faith in this director, who's utilizing his connection to actually bring out A-1's potential unlike certain ot*snip*. Should definitely check out the staff list from now on if you haven't already. I'm not going to call this the most "sakuga" anime of the season (
K has been managing to do each episode with only 6 gengashi only, which I think is a miracle), but Shinsekai is just full of pleasant surprises.