Unless you have a lot of space and disposable income, purchasing a stationary bike is not an essentially piece of exise equipment unless you really enjoy training on this machine.
The stationary bike is a good exercise option. But why not buy a real bike ? Besides the work you will be doing you will enjoy the pleasure of some nice views in front of you.
This depends on if you like biking or not. I personally love biking but have problems with my knees so can't ride a bike that long. Because of the pain I prefer to be on an elliptical machine.