Best Caster of these 3? Illya, Nursery Rhyme or Helena?

Um...casters aren't really best for Buster teams filled with berserkers, so I suggest Mash or a tank more, but to simply answer your question. If it's just a quick battle since it's filled with berserkers I suggest Helena since she can could pump buster damage, and increase NP of the whole team, so she'll benefit the berskers more than enough, but if you simply wish for a buster team with three buster NPs even though one of them wouldn't hurt as much as Herc and Kintoki, I think run Illya since her NP is a buster and stuff. Still since you asked for a Buster team I don't think running them would be good since they have three arts cards and wouldn't be pushing too much damage and the like.

Pretty much what he said but to add on, the current best buster support if you're going all in on the buster spam team would probably be Nightingale. And if you're going full buster you could just supply 3 quadruple or triple buster deck (including np) dps which would typically involve several berserkers. Casters are in the triple arts or quadruple arts set of cards.

Pretty much what they both said but to add on, if we ignore the buster thing, and try to choose which of those 3 is the best caster for like general usage... Probably Helena could be tossed into the biggest variety of teams. She can charge her teams NP gauges, and increase their quick/arts/buster, and she can even contribute some stars, so she can contribute *something* to any comp. She might not be the best choice for every comp, but it's pretty much impossible for her to be useless. Whereas Nursery and Illya both kind of have specialized uses, so they are both capable of being a complete waste of a servant slot in certain comps (such as a buster blitz team like you're running).

Pretty much what all three of them said but to add on, I think Nursery Rhyme on 2nd ascension form is the cutest. Followed by Illya on first ascension form(shoutouts to all my friends with an Illya not in 1st ascension form. you guys are breaking my heart :c ) Helena's on 3rd coz... yea.
All cute talk aside, I don't think any of them can go the buster support route. Helena's prolly the closest thing you'll have to one but it's not advisable imo.