Sounds like you don't know it yet, but you're in GREAT shape! You have a well-developed pedigree (going back to gt-gt grandparents and beyond), and the fact that they're all in America should make it pretty likely that you have plenty of relatives out there who have tested.
Right off the bat, you mentioned that you have a 2nd cousin match, on your paternal grandfather's side. So that means you can automatically (upon demonstration of the "paper trail" confirm back to, and including, your gt-grandparents on that side. The hardest part is making sense out of the directions!
That being said, it'd be best to look for suitable 3rd cousins on each of the 8 branches. If you confirm back to there, then the closer-in ancestors are "along for the ride" as far as also being confirmed. If you can't find that 3rd cousin, than you settle for a 2nd cousin, and can't confirm back as far (at least YET!).
Don't get too worried about YDNA. Mostly, it's just going to tell you which Berryann families you ARE distantly related to, and which you're NOT. It's cool to do, but it's more expensive, and isn't likely to do all that much for you that auDNA - that you've already done - isn't already going to do for you.
GEDmatch is of more interest, but is of secondary concern, I'd say. Get yourself confirmed out to your gt-gts first (and use your mom's to go a generation further back on her side, if you can). THEN look into triangulation, and GEDmatch, and mapping out what parts of your genes you got from whom, second.
That being said, sometimes its best to use a GEDmatch DNA match for your DNA confirmation, if that key 3rd cousin happens to be on there (or you can talk them into getting on there).
I hear the other sites allow you to upload an AncestryDNA test to their sites for free (or for a nominal fee, for full functionality). I've managed to keep busy enough with the AncestryDNA tests I'm looking at, that I haven't done that yet (but I do a LOT with this stuff).
Just make sure you mostly ignore the "ethnicity" stuff, for the most part. But it they tell you a "region", without giving you a percentage - THOSE can be extremely accurate.
Enjoy!!