To write php code all you need is a text editor. However a nice IDE greatly supports your code creation. Have a look at pepstorm.
Laravel is a php based framework. Find it at laravel.com.
For storing information a widely used database is MySql.
Software development requires versioning. The best versioning tool as far as I am concerned is git. You can find everything you need for git at git-scm.com
Nobody develops software on a live server, right! So you need a development environment. Docker is what you need then, easy to set up and maintain. See for yourself at docker.com.