Database server for log in and log out timekeeping hosting?

I am fairly new to hosting and server handling. I have been working for companies as a developer and every time I finish developing, my seniors take care of all the deployment to their servers (I am off limit to the servers).

Now, my situation changes when I got a job on a small company and they task me to develop a time keeping for them to be used because they use manually. They have two separate offices and needed the same database to store the employee time-in and time-outs. My question is what kind of hosting server should I use for in this scenario that is also ideal(Cloud or traditional web hosting or any suggestions)?

The database I am using for development is MySQL 5.7 and I used Laravel 5 as the web application to parse all the employee's time logs.

Thank you for answering me.