Frameworks when to use them?

Let me first clear clear something here, composer is a dependency manager, and twig is a template engine. Neither are really considered a "framework".

Composer is really beneficial on almost any project, with or without a framework as most projects will have dependencies. Twig can be beneficial on larger projects where views get more complicated. Twig is often used inside a framework, like Laravel.

Frameworks are fantastic if your app needs crud. (Create - Read - Update - Delete) features. A blog is a perfect candidate to use a framework. A basic, static php site would not need a framework. If you're database heavy, a framework can help tremendously here...if it's a small, light database than simple PDO will work.

As far as which frameworks to use, go with the flow. Currently Laravel, Lumen, and Slim are hot, and heavy development. That's what you want. I wouldn't personally recommend using a lesser none framework that it's in active development because of the possibilities of security vulnerabilities. Typically frameworks have a life cycle it seems. They're hot for a long time, and than the developer(s) loose interest in the project, and if the open source community decides to not carry it on, it kinda dies. You don't want a dead or dying framework.

The other is the weight of the framework. Lumen and Slim are lighter weight frameworks, with less features, for sites that don't need the everything and the kitchen sink. Laravel is a full stack framework with a lot of features, if that's what your site needs.