What WordPress themes or plugins can you use to create a 30-day challenge on a drip campaign?

You're going to need to baseline technologies - something to capture membership and manage members and something to deliver the content. Even in a low budget you can either merge to services/technologies or plugins together or find an all encompassing one. There are many more options than this but to help get you started.
Tools for Membership
- PMPro
- Woo Subscriptions
- Member Mouse

Tools for Drip Content
- Aweber, Mailchimp, Constant Contact, i.e. newsletter services with marketing automation built into them ('marketing automation' will be the keyword you'll want to do searches on to find the tool thats right for you)
- Intercom (not for low budget)
- Hubspot (not for low budget)

Tools that do both:
- Agile CRM (WordPress Plugin and Integration)
- Presspoint

Biggest thing to understand is that at the core you need two pieces - the first is a way to manage members (even if free) and provide secure content only to them. The second is distribute your content on a schedule. Like all things there are many ways to approach this but hopefully this gives you a head start. If you have more specific questions let me know.

I am a pretty big fan of the Sensei plugin from Woothemes that uses Woocommerce. Sensei is a paid plugin but its pretty powerful. You could use it for a content drip on your website and also set up courses. We have set up multiple websites using this plugin including using it to power an online driving school with prerequisites that have to be met before moving on to the next chapter and tests that won't let you proceed unless you get a passing grade.