Either direction is fine. If you start in the east, the first half of May is ideal for starting. If you start in the west, mid-June is good. I'd pick my direction based on the most convenient time for you to start. Personally, I like east-to-west.
You can fly on to Newport News, which is only 10 miles from the start. If you've never been to the U.S. before, you might like to visit Washington D.C. or New York City before heading down south.
No diversion necesssary for Yellowstone. It's already on the route. I would take the optional side trips noted on the ACA maps to Mammoth Cave and Jenny Lake if you have time, but I would otherwise stick to the route. The route has already been crafted to give you the best places to visit. Some people like to divert to the Katy Trail in Missouri, but the standard ACA route through the Ozarks is great as is.
The two main books on the TransAm are Donna Lynn Ikenberry's "Bicycling Coast to Coast". It's dated now (over 15 years old) but still worth reading. Just don't count on all the little details to still be accurate. The other book in Stephanie Kirz's "Bicycling the TransAm", which is good reference for motels if you plan to primarily stay in motels. I prefer Donna Lynn's book if you're only going to get one.
No "dodgy" sections at all. Wyoming is pretty desolate. Everything except Kansas and eastern Colorado is hilly.