Well, just managing and administering a dedicated server can be a full time job even if you are not running anything which may provide a return. There are a lot of issues which require constant monitoring and adjustments.
I guess you know that when you launch anything on the web, you are virtually running a place which operates 24/7 and as such is never closed.
Not just the web but any business venture would take a lot of hard work, dedication, determination, capital and know-how to make it work. It takes time to make yourself known and it takes time to get people to part with their money. Some business don't make their first sales even after 6 months on the job while some do. If you are prepared to work and take the risk, it could work out for you.
As to what kind of businesses, well the possibilities are endless. It is always best to work with something you know intimately about. You could survey the market and if you can sense a need which you can honestly fill then that is where you should go.