There are some free options for running a web server, as you’re doing this for fun and learning then just running a little service locally on your own machine might work for you, or another option is AWS, which has a 12 month free tier that would allow you to run a t2.micro instance, which is more than enough for what you’re looking at doing.
I am at little bias towards AWS as I have all my instances running there and it has been perfect for my stream analytics, but if you look around there are other providers that offer limited time free servers which if you’re just looking to learn and not go into production then they should all fit your needs.