How can I create a modern responsive sharepoint website that is for outside users, without looking like sharepoint?

I’m creating a website for a undergrad research project and have to use sharepoint. I have already come up with designers for the website and want to write custom hmtl/ css/ js code to implement all the design and necessary features. I will also need to use a server-side language to interact with a database as I will need student and teacher relational profiles. I have edited an .aspx page on sharepoint designer but when I test it – it doesn’t show the nav bar or anything. What is the best way to go about this? I know how to do this with regular code but don’t know how to do it with sharepoint. Maybe sharepoint designer? Looking for the best way to create a good looking website. Thanks in advance for any suggestions.