I understand that you are asking about the cost of hardware. If yes, then there is no one good answer. It all depends on what you want to use it for. You can build one for as low as a couple hundred bucks, or you can spend $20K or more. I wouldn’t suppose the actual server would be your bottleneck. At least not if you get fairly recent hardware.
But I think serving on from your personal account presents some issues. Among them issues such as:
upstream speed Most home connections offer somewhere around 384kbps upstream which is OK for small sites, not too graphics intensive. I run a small server from home on a 640 upstream. With some cable providers there is an option of 1.5mbps (i.e. close to T1) or more upstream, at extra cost. My existing connection costs roughly US$35.00/mo, the 1.5mbps would double the cost, which would still make it fairly reasonable.
inability to use certain ports
Most ISPs block some ports commonly used by servers. Specifically port 25 is a problem. It is blocked by most ISPs which makes it hard (but not impossible) to run your own email service.
dynamic IP
Kinda hard to make sure your site is always found by DNS. You would have to either monitor it personally or pay fo some sort of extra service to do it for you. About the only decent solution is to get a business class service, which is usually more costly but offers a static IP.
Monthly transfer
People often don’t realize that ome ISPs impose limits on monthly transfer. My cable co. gives me 15GB/mo which is enough for my low trafficc sites and 3 persons at home using the internet, but I still hover around 13 to 14 GB monthly usage, so the margin of comfort isn’t too large. If you're planning a decent web service this limitation may be a pretty tough problem – you will either pay through your nose for extra bandwidth, or you will get canned for using you home service to serve web pages (forbidden by many ISPs)
I heard some DSL services offer unlimited transfer but reliability of DSL depends on your geographic location more so than it is in the case of cable service. I live about 3.5km (just over 2 miles) from the nearest DSL switch. Max distance is 4km so understandably the quality of DSL in my area is unacceptable.
These are the negatives but of course there are benefits to running a server from home. These I believe don’t need to be listed.
My $0
