Occasionally, certain kinds of exploits will require a server to connect back to. Some examples are connect back shellcode, cross site request forgery (CSRF), or blind cross site scripting (XSS).
If you just need a web server to host simple static websites or check access logs, we recommend using PythonAnywhere to host a simple web application. You can program a simple web application in popular Python web frameworks (e.g. Flask) and host it there for free.
If you need a real server (perhaps to run complex calculations or for shellcode to connect back to), we recommend DigitalOcean. DigitalOcean has a cheap $5/month plan for a small server that can be freely configured to do whatever you need.
We use DigitalOcean to host a large amount of our online presence. The above DigitalOcean links are referral links and we may earn affiliate hosting credits if you register through our link.