Hello,
First let me say that I know ZERO about Sony cameras & lenses. I am a canon guy.
I have a friend whose wife owns a Sony A200. He came to me for lens recommendations. I told him I don't know Sony lenses, but I did give him some general advice based on my knowledge of canon, and I know this great resource (this forum).

He is wanting a zoom lens (he mentioned a 75-300mm), so that is close to the range he is looking for.

I told him that Image Stablization (don't know what Sony calls it) is a very important item to have. Also a good focus motor system (canon's best is the Ring USM - Ultrasonic Motor), which I also don't know Sony's equalivant. Water sealed.

He said he is willing to spend some money for a good one, but like everyone, he wants the best value for his money.

His wife shoots action, sports, kids at play, etc that she would need this lens for.

Thanks for any advice you can give.