- If you're in the EU, metcup is priced well and competent. If you're somewhere else, I got no idea.
- Not really, just preference. Often some of them are just more expensive than others, both to register and to maintain. Some don't support DNSSEC (really) which you really don't need to care about, but it's a difference that may exist.
- Literally any age. The older it is, the less it can do and/or the more power it'll use to do it. Depending on where you are and now specifically what you pay for electricity, using a newer system can quickly pay off. Most things in the list you gave aren't 'intensive' to host, but depending on features enabled immich can at least at times require some CPU and memory. The rest can run on a raspi (meaning literally any PC will do as well).
- If you're hosting on an old PC (x86), I would suggest going with a hypervisor (proxmox is popular for good reason), and then hosting everything else as a lxc or VM. If you want to actively do things by hand, to learn or just experiment, use Debian. It's the most common server operating system used, and will often be the assumed default for guides or installation instructions.
Whatever you pick, do not install everything just onto "the server". Pick some form of abstraction (VM, lxc, docker, kubernetes, ...) to isolate and manage your services.
Important: do not host your own email, ever. Let alone as a beginner project. You can host it behind a forwarder that acts as the destination for the other mail providers, but don't have a public facing, DNS registered mail server (neither at home, nor as a vps or something). It will cause nothing but problems. You will regret it. Quickly.