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?
Say: let them use a web app?
That’s a REALLY broad definition.
A web app that does what?
Are you running your own Netflix-ish server? Transaction processing? Cloud storage? Ai chatbot?
Each one has very different requirements, and this is just the first four that came to mind .
AWS has hundreds of buildings filled with millions of servers, so you aren’t going to compete with that, even on a small scale.
But could you run your own little Facebook type thing? For a handful of users, sure. Could you handle the number of users that Facebook actually has in a day? You are looking at buildings filled with Computers, not a single machine’s spec 
Generally speaking, not a well-advised idea, especially for someone who has to ask how to do it (truly not being snarky).
I was a cisco instructor in the 90’s, (so teaching networking and security were my bread and butter for a while) and I wouldn’t think of doing this - except… If the only access was via a mesh network client such as Tails/Tailscale, the server was dedicated to just this purpose, it was isolated on its own LAN segment/DMZ with no routing path to my home network segment, the server was not Windows, but Linux, and I had a robust backup plan, access control plan, and access monitoring with alerts.
There’s just too much risk exposing a port to the world.
If you’re only accessing the server remotely via Tailscale and no ports are open, is it necessary to have the server on its own isolated VLAN? I like accessing my server locally most of the time and via Tailscale when I’m out and about.
I’d still do this.
Security isn’t one thing, it’s layers. So if any single layer fails another still prevents access.
With just Tails, if a bad actor gets access via a compromised user machine, they could potentially get access to the rest of your network. If the server is on an isolated Lan, there’s nothing for them to access - it’s a rock-solid guarantee that the most they can do is damage to that server and network segment.
We (us IT folks) see users get compromised almost daily, largely through social engineering. It’s a huge risk.
And it’s trivial to have something on its own Lan segment.
You can host most basic web apps off a raspberry pi. You just need to:
.
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
If you let random people install stuff on your server all you get is assholes install monero miners to gain 1 cent from you wasting 30 dollars in electricity