We have consignment stores around here that have nice quality, gently worn, name brand coats in your price range. Perhaps you have them in your area, too.
A wool coat in a dark color won't show everyday smudges, like car dirt and little hand prints. You can dry clean yourself using those bags you put in the dryer and take it in to the dry cleaners once at the end of the season.
I had a synthetic camel coat that everyone thought was real. But I still had it dry cleaned because it would have lost its shape if washed in water, even carefully by hand.