What do I need to make a website that references a table of anonymous users to notify using SMS?

Question

This is a project I'm working on for use between people at my university. The idea is simple, it's a website where people can submit anonymous comments to other people based on a unique identifier, which is just a random number. People sign up with their unique identifier and their phone number, which would be saved together. Other people hop on the website and submit a comment with the unique identifier, which is sent via SMS to the corresponding phone number.

Conceptually I feel like this should be easy, the website just searches a table for the identifier and then uses an SMS API to send a message to the associated phone number. Also dynamically adds new lines to the table as people register.

I am real new to web development (if you couldn't tell), but I'm not afraid of a little code so I'm figuring it out. My problem is I have no idea big-picture-wise what building blocks I need to connect together. I think I found a good service called Twilio for the SMS API. I think I need to pay for web hosting, but do I need to rent server time? It's a real simple operation but the data also needs somewhere to live. I want it to be a long-term installation so I don't want to host it myself.

I would be very grateful if someone could real quick make a shopping list of the components I need to make this happen, or just any other tips if you've got 'em