What’s the best way to integrate with Mailchimp? Can it be easily done with the standard IP tools or will I need to purchase a plugin, and if so what would you recommend?

Would be great if I could create and automatically update lists based on member groups and purchase history etc

There is no built in Mailchimp integration I'm afraid.

Would be great if there was a fix for this. Zapier does not support IPB as yet.

I use a MailChimp plugin that has worked great for me!  Check it out in the Marketplace.