I use a atom based system for my homeserver with ubuntu server on it.It runs fine with apache on it , other things i use it for are file sharing and i run a torrent client with a webinterface on my home server. The system will cost around 200 dollars (motherboard, memory, hardisk, case, psu). It makes almost no noise i got one 40 mm fan in my case. You could run it fanless but with a litle fan is better for cooling and it makes almost no noise my hardisk makes more noise than the fan.
Specs of the machine are:
Motherboard: Intel Desktop Board D525MW Innovation Series (fanless)
CPU: Intel Atom D525 1.8 Ghz dual core
Memory: 2 GB DDR3
PSU: PicoPsu 65 watt
Hardisk: 320 GB laptop hardisk (2.5 inch)
As os i think debian or ubuntu server are the best choice (they are almost the same ubuntu is based on debian), CentOS also is realy nice i realy like the way how to manage it and the documentation and support on there site is great only downside is that there is less software and older versions of the available software in the repository's(this makes it more secure). I heard it uses a bit more resources from your system don't know if thats true i never instaled it on my homeserver only used it for a school project.