There are many others, search the Internet for more options (and more confusion)...
Once you have access to your own root (Administrator) account of a web server, you can set up the web server, upload your web application files and setup its settings, and let the web application run 24/7
But once a while, you have to maintain your web server as no one else will (or can) do it for you, failing which your web server (and thus your web application) performance will gets slower and slower and its security will get more and more compromised
Web Server Setup
Focus on LAMP Stack
LAMP = Linux, Apache, MySQL, and PHP
For this lecture note, we will not digress too much and talk about many other web server options out there that I have not tried (WA/IMP*, MEAN, etc)...
Choice of Linux distro (Ubuntu, Debian, CentOS, Fedora, etc...) or from a software bundle (this will save you time from installing the "AMP" component yourself) — unfortunately there is no Laravel one-click-app yet...
How much do you want to pay per month (or per hour)
Data center region (where your main* web application visitors are geographically located)...
You can now host your web application by copying/uploading your web application files to a certain designated document directory (depends on your Apache setting, the default for Ubuntu 16.04 LTS is /var/www/html)
The index.html (or index.php) stored in that directory is is the one that will be served when you entered the IP address of your Digital Ocean's droplet in a web browser, e.g. visit http://126.96.36.199 (we will talk about Domain Name registration in the next lecture)
Maintenance - Linux Specific
Every year, there are various (new) Linux distro released to public, e.g. the 2016 version
Upgrading the OS (the "L" in the LAMP stack) will likely entail the need of upgrading everything else (the "AMP"), so do such upgrade when there is a (critical) security upgrade (painful verbal story in class)...
As root, you can perform these tasks (not exhaustive):