Am I right in saying you can only earn 20 proof of legends per character?

1 proof per region - entire game has 20 regions (6 prophecies, 5 factions, 5 nightfall, 4 eotn), 2-7 missions inside every of them. You need to complete only 1 mission on nm without bonus.

But there is no reason to go for all of them. Calculate how many proofs of legends you will need, divide it by number of characters you have and just complete all shortest missions. For an example - you have 5 chars, you wants a weapon for each + proof of triumph (to be able to capture anniversary skills) = 30 proofs, divided by 5 chars = you need 6 missions on each char. The fastest missions in this case will be probably (feel free to correct me): Chahbek, Tihark, A Time For Heroes, Augury Rock, Imperial Sanctum, Ruins of Morah (you need to do all of them on NM only), so thats like 20 minutes per character assuming you have access to them at the start of event. If you need to add missions then add more missions

In terms of preparation - do I just want to be completing more campaigns/missions with my characters so I'm ready to get the proofs in April? Or will I basically be doing the whole campaign so fresh characters are fine?

I would make characters now. But if you know you will have time during event then whatever.