Normally, I would say Cave, but this week's events are Lucky Board. The price for medium threads in this event are very cheap.

With 4k coupons/ingots, it should be relatively easy for you to buy all 200 medium threads, which should also come with a hefty amount of rewards from the Lucky Board. At that point, it's up to you to spend it on Cave, or to spend it buying refines or character frags in Lucky Board. But get your BA to rank 4, at the very least

It's up to you. I don't know how close you are to Rank 4 BA, but even 200 threads won't bring you far enough to get rank 5 BA.

Honestly, if it were me, I'd redeem 200 medium threads and 200 medium refine scrolls. The former, I'd use until I got rank 4 BA, then save the rest for the next rebate. The latter, I'd keep until the next refine event (and there's always been one once a month).

With my remaining coupons, I'd * it all on Lucky Board and pick up as many Cursed Hidan frags as I can (since I don't have him). This event is just too good to pass up. You can get lvl 3-4-5 magatama from the Ninja Packs, and depending on where you land, seal scrolls for as cheap as 20 coupons. It's great.

If you already have Cursed Hidan, then, and only then, would I spend on Cave. The cave function isn't going anytime soon, so there's really no need to * your coupons on it. I would just slowly save up keys from various different weekly events and spend them 50 at a time.
If, for some reason, you really want to spend on cave, spend just enough to get at least lvl 2 runes on everyone, then stop lol. That alone should be a nice power boost

That's the thing though. There's no guarantee you'll get those Initiative and Crit runes..

I spent 20 cave keys that I picked up from the last Missions event and got two lvl 1 initiative runes total. That's puny.
But then again, I got 3 purification runes and a dango so I might have just been really unlucky, as always... :'(

It's up to you. Most of this game is a gamble, after all.