When I tour in the UK (3 tours in the past 10 years), I get the AAA maps and try to find the smallest roads to ride on. I also spend a lot of time asking locals, via couchsurfing, warmshowers, and CTC forums, about various roads and routes. I have ridden on CTC routes and liked them, as well, though I prefer pavement to the dirt paths often used by the CTC.
The US is simply too big to have one map booklet for the entire country at the 3 miles = 1 inch scale. In fact, most states are too big for that kind of treatment and who needs all the roads in Kansas when all I might need is a safe biking route through the state?
Were I to do a cross-country trip, I would start with the ACA routes and then decide if there are reasons to deviate from them, such as friends, places I want to see, or better routing suggestions from here or crazyguyonabike.
When I have ridden on the ACA routes, I have found their maps indispensable, both for planning where to stay and for actually navigating while riding and I would recommend them without reservation if you are using one of their routes. Keep in mind, they come in sections, so you can ride a section and then go your own way. It isn't all or nothing.
My advice would be
1) look on the ACA site to see where the cross-country routes go and decide if that is where you want to ride.
2) If doing an ACA route, look for used maps (if new is too expensive--note joining gets you a discount) at crazyguyonabike.com. Be aware that you want the latest ones, so know what the latest ones are if you are buying used. The ACA site tells you how to determine when a map was printed.
3) Look at the states you are riding through for state bike maps. This site is a search engine for state and local bike maps:
http://www.bicyclinginfo.org/bikemore/map.cfm . Here are
35 links to US bike map sites, states, counties and cities.
4) Ask here and crazyguyonabike.com for specific advice about roads and routes. I'd try to create a route first, before doing this as it is easier for someone to answer a specific question about a road then a general one.
In the US, it can be hard to determine if a road is busy, has a shoulder (though Google Maps helps here), and is suitable for biking just by looking on a map.