The folding requirement narrows down the field significantly, but great quality choices remain. I’m not sure if you’re aware, but a folding bike with smaller diameter wheels and tires will handle a bit different than what you may have been learning on. The folder will be more… nimble. I wouldn’t consider the difference in handling a dealbreaker by any means. A quality folding bike can be spec’d and outfitted for any purpose, just like any full sized bicycle.
Folders are gender neutral and typically offer a very wide range of adjustments so fitting your bike will be no trouble either. Your price range is appropriate for a good quality folder, leaving money for the important accessories like a helmet, lock, racks, lights, etc. One important consideration with folding bikes is their weight — not because you’re trying to race or be one of the cool kids, but the premise of a folder is portability and if you’re planning on carrying it up stairs, well, only you know what you can handle.
Brompton, Tern, Dahon, and Bike Friday are good places to start your search.