Your programs running will determine your hardware. But generally speaking if you don't have some very specialized needs just about any old hunk of junk will run a web server. It doesn't take a lot to serve low traffic websites.
As for the processes running, that's a given. You need to look at every single process that's running and determine why you need it. If you don't need it, get rid of it. It's a black and white choice. Bluetooth? not on a webserver. Sound program? not on a webserver. and so on. You need to do this anyway, it's just a good server security/admin practice. Only ever run the bare minimum programs that you need. Everything else is off. (To look at it another way, turn everything off. Then add only the stuff you need).
Where did you get this process list? Asterisk for example is a digital PBX. It shouldn't be running on 99.8% of the webservers around.
You should ask your question the other way around: "What are the minimal processes needed to run a secure webserver", because the less processes are running, the less entry points potential hackers have to access your system.