Welcome to astronomy. I have written several articles to help you.
How to choose the right telescope
Telescope First Questions
Ten Telescope Eyepiece Questions
Once you have your telescope:
A Dozen Telescope Observing Tips
The best bang for the buck is a matter of your personal preferences as to features and observing situation. In terms of the biggest scope per dollar, tough to beat the Bushnell DOB6
Yes, you can see exactly the same types of objects with a small telescope as with a big telescope. The difference is that a big telescope can see more of these objects and more detail in the objects. 6" though, is a respectable size in a telescope and really an excellent size for a beginner.