My usual approach to web(sites)
I make various websites (such as this one) for personal and professional reasons. My standard stack is (Python) Google App Engine (mainly because it makes a bunch of tricky and important things really easy, for example: security/users, scalable storage, deployment/configuration; so you can focus on actually solving problems) with Bootstrap. I'm will probably start using Flask (with App Engine) as the default framework isn't great once the site grows a bit. There is a GitHub project I plan to look at.
I also recommend using Yeoman/Grunt/Bower to set up projects, manage dependencies and compile/test things. Obviously, you should use version control too.
Some tips on creating Web Apps for iOS, Firefox OS and Chrome.
Just Use Bootstrap 3
For web projects just use Bootstrap 3 (unless you want to increase billable hours).
Google App Engine
Some thoughts on Google App Engine, the platform on which this site it built.