A quick look at the installation documentation shows the minimum required software - at the very least, PHP and some extensions.
https://laravel.com/docs/5.6/installation
If you're using MySQL or Redis or anything else then you should be aware of that in your application and know what you need. You'd also need a web server more than likely, Nginx or Apache2 are supported by Laravel out-of-the-box. You can use whatever operating system you want that fits these other software requirements, often people choose a Linux distribution such as Ubuntu.
Hardware details are another concern entirely, that depends on what kind of traffic you're expecting, what kind of processing your application has to do, etc. It's very different if you have to encode 2GB video files from millions of users compared to a simple web page with static HTML and a form. More than likely any $5/month server like DigitalOcean offers will suffice a small application for few people.
