Trade in before the event ends just to be safe...last time the trading post was still trading shards after the event ended but who knows if they'll do that again. Personally, I would get card reveals and use them when you want to try and get slayer cards, and stockpile some wilds to level them. If you really don't care about slayers, getting just SR Wilds would make more sense. 1400 shards spent on wilds and used on some high SED girls will increase your SED by around 10-11K, whereas spending a large amount to get the SR at ~1250 SED and using the remaining shards on SR Wilds won't net that much of an increase. Same with getting the Rs and R Wilds, they won't give you as much total SED. The H scenes will be (if they're not already) on the Wiki if your curious about those so I don't think the cards are as useful as the other rewards. If you haven't done so already, this would be a great time to use your wilds to start levelling up your Moes to 60 for the most SED.
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Your total SED (ALL cards you own) will come into play during another type of event, the Elite Guard, so yeah try and get as much SED out of all the cards you own as possible. The cards on your homepage display are really only for show, doesn't matter what you put there, it has no effect on gameplay. The PeroColo deck is seperate from the homepage display, so continue to use only the strongest cards in PeroColo.
The difference between card types: Moes get a lot of SED per level until ~60 and past 80 it's practically nothing, they also have to lowest total SEDs. Sexy barely gets any SED per level until past 80, they also tend to have the highest SED...except a few which I just happened to make a thread to rant about. Babes have in the middle SED and they level up linearly, ~1 percent of their total SED per level.