Sure you can! It all depends on how you configure the Pi. I can see ye'old good LAMP answers already creeping up... I would strongly suggest to stay away from Apache traditional full PHP (CPU & RAM HOGGERS)
This is a fact: Instead for your front end you should must use nginx instead. It was designed for embedded devices and runs extremely well on the Pi, especially the 3.
The back end is all up to you but In My Honest Opinion
- Python is Pi's programming language. If you know Python then use it. Plus there allot of frameworks in Python for creating websites easily.
- I would suggest Node.JS since it is extremely lightweight but you need to learn it. Node.JS was built to handle a ton of connections easily.
- My self on the other hand being a .NET G33K - I host .NET MVC websites because I can build and deploy them rapidly on my dev machine. Hosted behind nginx they run just f***king great (I cant even believe how great they run it blows my mind) and as of 2018 Dotnet Core 2.1+ can build native libraries that do not need any extra SDK's installed on many Linux distros, including Raspbian.
In terms of SQL storage... You can do MySQL if you feel like you need a fully featured SQL database engine but you can get away with SQLlite really easily now a days too.