I'm using the second version of the plugin. I did make some progress as I was taking screenshots. I did not have a price set in Akeeba and I believe that is what was causing the issue. Here is my setup now.
1) Go to Akeeba Subscriptions and add (1) 30 day product and (1) 365 day product (capture1.png). Make sure to set prices (capture2.png).
2) Add a characteristic (Product -> Characteristic) called "Payment Terms" and two values "Monthly" and "Yearly".( capture3.png, capture4.png).
3) Add a product for your membership type, in my case "Student Membership". (capture5.png).
4) Add characteristics, set the default characteristic, in my case "Monthly", add the price for default (capture6.png)
5) Make sure to pick the subscription level (capture7,png).
6) Click Manage Characteristics then click on a characteristic and (capture8.png).
7) Set the price and subscription level for each characteristic (capture9.png, capture10.png).
You should know have a product with two different payment terms.
To add more payment terms (e.g. Quarterly, Semi-Annual, etc) repeat step 1, edit at step 2, and repeat steps 6 and 7 for each product.