You can see your new matches. There are 2 ways to sort all of your matches. By relationship and by date added. Click on the Date link just above your first match on page 1. It will sort the matches in reverse order by the date they were added.

I agree that folders would be nice. I use the notes field. If you install Jeff Snavely's AncestryDNA Helper you can search your notes and bring up a list of matches with a surname or any other keyword you're using in the notes.