This question pops up fairly regularly, so you might want to search previous iterations.
Verizon is generally acknowledged to have the best nationwide coverage for cyclists, including small towns. You will want to note that Verizon doesn't use GSM, so your German / European phone won't work on Verizon. You can, however, buy a pre-paid phone fairly inexpensively once you arrive (check with the large chain discount stores).
AT&T seems to be second best, and they do use GSM. I don't know the details of how to get "turned on" coming from outside the country, though.
Don't expect any cell provider to provide seamless coverage. Out in the woods, or out on the plains, you can find plenty of spots that are more than 5 miles from the nearest cell tower = no coverage. As I noted above, Verizon does have towers in most small towns, and strangely enough almost all the way across Kansas. But if you leave the beaten track, and especially if you take small state or county roads, or even Forest Service roads, through the mountains, your phone will drop coverage.