HTML and a server side solution aren't mutually exclusive technologies (in other words you will need both). Handling financial transactions, from a development perspective, can be challenging and getting it wrong can lead to serious issues. It sounds like you might have a long road ahead, have you considered using a pre-existing solution instead of rolling your own? There are open source solutions liie OSCommerce, or higher level technologies like Ebay shops that might serve your needs more quickly than learning how to implement your own solution.
To specifically answer your question: Asp.net, or PHP or Java etc, is the server side technology that implements your commerce site. HTML is what this server technology sends to the customer's browser (the client) to be rendered. Whatever approach you take for a server solution, you will be sending HTML. Your server logic must implement payment functionality if you want to sell stuff. You can usually delegate this to a professional service like Paypal, however even coding this handover of responsibility can be challenging and must be done perfectly (for obvious reasons).