First of all, as a beginner, going out a buy a new racquet would a bit of a waste of $$$$.
There is nothing wrong with the Wilson Prostaff 6.6 that a few lessons, and some new string wouldn't cure. That would be my recommendation. New (less tight) string would cost around $30.
Then as you develop a playing style, or an awareness of what you dislike about the Pro Staff, you can more intelligently look for a new frame.
The most important question to answer in changing racquets is "why?". What do you not get in your currrent frame that causes you to go fishing? Does it lack power, or have too much? Is it too heavy, or too light? Sometimes these issues can be solved with new, or better string, or a different tension. Like the power. Then you need to begin to educate yourself with regard to head light/head heavy to understand what these concepts will give you. Do you want heavy frame (around 11.5-12 lbs) or a light one (around 10-11 lbs). There are trade offs. Heavy frames will be sluggish, but give you free power. Once you get them going it doesn't take much effort to make the ball go. Lighter racquets will need more swing, and more racquet head speed, but will be very maneuverable and feel a bit better. Typically light racquets will be head heavy, and heavy racquets head light, but not always. There is a term called swingweight which is essentially the mass of the racquet in motion. But it's all meaningless if you don't know what you want/don't want in a frame, and you won't know that until you've hacked around a bit.
As for where would you start when you do start looking for a new frame, you've nailed it. TW demo program, or a similar demo program at your local tennis shop. Usually they will charge you like $10-$15 to take out 2 or 3 frames at a time to make a comparison.