What form would be accomodate my online booking needs?

I have a business currently online that I will be moving from Weebly to Shopify. Can you please have a look at this particular page: http://www.byronbabyshop.com.au/holiday-hire.html

What I want to keep on the page is the list of items with the check boxes and the contact form for customers. BUT what I want to add is a online booking system where they can book multiple items without going to a new page for each item they tick. I would like the tick boxes to add up to the total cost of the order for the customer to view.
This booking system will allow customers to pay online if they would prefer or we can have our customer service team call them back. As we are a hire business, I will need to be able to hold credit card details as security until the end of the hire period so this ability in the system is also important.

I assume that you are referring to an order form with payment integrations.

You may collect customer information, allow them to choose from your multiple products and see the total cost of their order using JotForm payment integrations.

Please check the guides below to learn how to create your online booking forms 

https://www.jotform.com/help/2-How-to-Create-Your-First-Web-Form 

https://www.jotform.com/help/25-Setting-Up-Email-Notifications 

https://www.jotform.com/help/47-Order-Form-Basics 

https://www.jotform.com/help/49-Order-Form-Types 

Once you created your form you can embed your form to your website as well:

https://www.jotform.com/help/34-Adding-a-Form-to-a-Web-Page 

https://www.jotform.com/help/67-Which-Form-Embed-Code-Should-I-Use 

If you have any questions, please let us know.