Honestly, trying to host a server when you aren't a sysadmin can be a total headache. For just you and your mates, you really dont need a massive setup. I would suggest looking into a managed VPS provider so you arent stuck fighting the command line for hours. Just be careful though, because some of the cheapest options give you zero support if things break. I have had solid luck with Linode Nanode 1GB RAM 1 vCPU servers for small projects like this. Its well under your ten bucks budget and gives you enough juice to keep the latency low since you can pick a London data center. Make sure to watch a basic guide on setting up a firewall, though. You dont want to leave your server wide open to the entire internet the second you turn it on. If you go with something like DigitalOcean Droplet 1GB RAM 25GB SSD, they have a really decent web interface that makes the technical side way less scary than a raw dedicated server. Just keep in mind that you are responsible for the backups yourself, so maybe set a reminder to do that manually every week. It might seem like a lot right now, but once you get it up and running it basically just stays stable on its own.

Jumping in here because I remember how confusing this stuff was when I started. Honestly, skip the VPS route if you dont want a headache. I had a way better time using BisectHosting Budget Plan 2GB RAM for my group. It costs way under ten bucks and basically acts like a plug-and-play panel. You just click start and you're good to go. Another solid pick is Sparked Host Budget Minecraft Hosting 2GB RAM. They have really decent support for newcomers, which is a lifesaver when things go sideways. You get a clean interface instead of typing commands into a black box all night. Just keep your mod count low if you go with the base tier, but for a group of four, it should be smooth sailing.

In my experience, if you want something that just works without the server maintenance, look at Oracle Cloud Always Free Tier which gives you a decent ARM instance for free. If you want a bit more power, grab a Hetzner Cloud CX22 4GB RAM 2 vCPU 40GB SSD instance for like five bucks. It is super stable for small groups, and the performance is way better than those overpriced managed options people usually push on beginners.