Straight off, I'd advise you hop along and grab a good working Gallery module (I went for the subscription at smcculloch.net and have enjoyed good progress and interaction with the developer and other users).

Then, to deal with your user permissions... Create your new user role e.g. "GalleryViewer". Add that role to your user. Create a page, only tick that user as the role that can view the page.

Alternatively, let all users view the page, but go into the module's settings and override the view permissions - set it so only your desired role can see the module.

Alternatively, If you have the gallery module I suggested above, you can use its settings page to apply permissions to specific roles.

Depending on how you are organising viewing and uploading permissions, you should be able to make the heirarchy of page viewing, module viewing, module editing, and then the module's own settings to make it work how you want.

Good luck
Rob