Switch from file_picker package to first-party file_selector and/or image_picker

[gnprice]

As described at #114 (comment) ,

now we may be able to replace both uses of file_picker with first-party plugins

namely package:file_selector and package:image_picker.

We didn't use those initially because they didn't at the time have all the features we need. It looks like they now do.

Meanwhile the third-party package:file_picker seems to not be vigorously maintained. For example see:

• Plugin "default implementation" warnings on latest Flutter #825

[Kavan2003]

Hey, I would like to work on this project.