First, I have to commend you for not advertising and pushing it in my face. I see a way to become a member, but I'd like a breakdown, and I can't find it. Like are there a certain number of coins and such per month you receive? I've been trying to find a list of benefits but couldn't, so again, thanks for not pushing it on us, but also, maybe make it a little easier to find for those of us interested.

tldr; what are the benefits of joining? are there periodical coin drops?

The benefits for members are mainly extra options for creating games, though members also get other perks like early access to new modes, like when Idle was first pushed. No coins are given freely through memberships.

Members can also use Autopilot, which lets AI do orders for them and can disable ads

Members can post images in forum, use commander, special cards. They have more vacations.
Mainly stuff in https://www.warzone.com/Membership

You don’t get periodical coin drops (you can get free from raffle and wheel or from coin games and tournies, which could be used to buy membership)

Membership allows you to use autopilot (in my opinion the best feature), commanders, bomb cards and mods in games, access to the standalone client, the ability to to post inline images in the forum and access to the recent games and fun stats page.

No coinage per month means I won't sign up. Just saying. I'm contributing. I know how this game works and don't care. Throw me a bone.

if you want membership but dont want to pay coins you can try https://www.warzone.com/Purchase?item=Membership.

on a daily basis

I really like this page https://www.warzone.com/Unlockables for seeing what gives you what :)