I'd like to have my own server at home sorta like a home AWS.
How to set up one and make it available to anyone over the Internet? What tech specs should I buy (RAM, CPU, # of cores, operating system, etc.)?
How much does it cost to keep one running all the time?
You can host most basic web apps off a raspberry pi. You just need to:
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Edit: BearOfaTime brings up a great point. I'm telling you how to do what you asked but you probably shouldn't. If you do, try to airgap the server from your personal network as best as you can
Edit edit: You know people will let you use their servers for small projects for free right? Check out https://ctrl-c.club/#what or hang out in the LowEndTalk forums and provide quality input and enter some of the giveaways for server space
Although the drawback to ctrl-c club is that you're not going to get full control of how you install libraries and applications