Free optionsIf your loading screen is just a static html page, consider using
GitHub pages. GitHub is fast and quite reliable.
If you need a webhost that supports PHP, MySQL and other fancy stuff, take a look at
HelioHost.
Paid optionsElpishost. Haven't used them. Heard great things about them.
If you're feeling adventurous, set up your own web server! It's a fun, educational and reliable way to host your websites.
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Ramnode starts at $15/year. They are my personal favourite. I use their servers to host all my websites and gameservers. They have a tutorial on
how to set up your own web server to get you started.
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Vultr starts at $2.50/month. I mainly use their servers for testing. Their servers have great performance! They have an amazing tutorial on
how to set up a web server too.