I'm not sure what your idea of 'cheap' is when it comes to dedicated servers. If you want professional, then you should go with a company such as LiquidWeb which offers single processor/multi core dedicated servers for $179 a month. I've heard rumors that some hosting companies offer dedicated hosting for as little as $30, but never actually found one for myself.
There are already many well-established web hosting firms nowadays that offer affordable web site hosting plans with excellent capacity and quality. This just gets to show that the market of budgeted web hosting is lively and competitive.