That really depends my photographer had a special at the time which included the engagement photos. I had been quoted by a friend who does photography $275 which I found extremely expensive for someone who isn't a professional. Other photographers quoted me at $280 $300 and $350 they are all around that price. Also it depends in your area.
We paid $112 for 4 hours. She traveled to our desired location, took 700+ shots, and gave us 180 edited pics. Since then, everyone who has seen our pics, also asks us for her info to hire her. Her work is amazing! She has raised her prices I think.
As a photographer and a future bride, as with anything, you get what you pay for. Sometimes you can find a beginner with talent for very cheap but oftentimes you will sacrifice quality. For a good engagement session depending on your area you could pay anywhere from 150-500... It also depends what you get out of it. Are digital files or prints included, or is it just a session fee?
I would say that $300 is pushing it, but thats the most that you should expect to pay. Ours were part of the package for the wedding so I can't remember the exact cost breakdown but it wasn't any more than that