I would build the website from scratch. This would include -:

- Design of the website structure and its applications/functionality

- Interface with 3rd party applications (APIs or embedded apps) 

- Hosting website on chosen platform and Maintaining website functionality

Apart from simple website which just display information, I can also offer to build web applications for -:

- Data Analysis and visualization

- Payment Gateways

- Marketing research applications

- Games and Art/Design applications

While I'm always upgrading my skills and tech knowledge, these are some of the technologies I am femiliar with (5+ years experience) -:

HTML/CSS/Javascript

PHP/ASP

React/Vue.js

Matlab (and its toolboxes)

Python and its libraries

SQL