I don't think it is that bad an idea to be honest, although I think it would be cheaper buying a shared hosting account (Just a few $) compared to even just the electricity etc. required to keep your computer on 24/7
If it is a DSL connection it would be on 24/7 anyway but you would have to keep the computer on 24/7 now.
Of course, you couldn't run a very big site from your own computer because of the connection, but you could run a small personal site without many problems.
I know people that have done this (Not personally) and it worked out ok for them. It can be a good experience if you are interested in running a server.
As Lesli said, you could do a course, but I would only suggest that if you are looking to do it as a business or you are very serious about it.
Most people would just do it from their home computer for experience or because they have a small personal site that they like to run and it may be easier to do it all from the one computer which you have access to 24/7.
You might also need something that requires root access to the server meaning you would either have to get a VPS (Virtual Private Server) or Dedicated server, so it could be cheaper running it from your own computer.
You also don't have the restrictions which you would have on a VPS and sometimes even a dedicated (Depending on the data center)
Security could be a problem but again, I don't think it would be that bad since it is just your own sites you are running and they may not be very big with a lot of visitors.
Xitami is a very simple program, just basically install it and run it which takes very few minutes, then you put your .html file in the correct folder and away you go.. for the most part anyway.