Half hour missions are always more efficient within their rarity. Use some simple math for your best option, like a rare 1-hour is a little better than a common half hour. I would jump on missions that give multipliers regardless of efficiency, normally, but at this point you probably don't have the time to get a girl if you do so.
I haven't used many keys just for gems, but my experience is about 20 gems for 200 keys with the biggest chests. The key decoration is definitely worth maxing, even aside from gems keys gate all the porn and most of the story. The only thing that affects chests is company level.
Sacred Sword Princesses invite code for server 2: Ruu0006963