How can I cut off the number of options?

For instance, I would like each option to only be chosen up to 30 times. 

You cannot do this with our basic fields such as the dropdown, checkbox, and radio button fields. You will have to use any of the following widgets:

https://widgets.jotform.com/widget/gift_registry 

https://widgets.jotform.com/widget/ticket_purchases 

https://widgets.jotform.com/widget/appointment_slots 

Guide:

https://www.jotform.com/help/282-How-to-Set-Up-the-Configurable-List-Widget