Alltel piggybacks on Sprint and Verizon no more than Sprint and Verizon must piggyback on Alltel for their 'nationwide coverage.' There would be vast areas around the country where Sprint and Verizon would have no signal if it weren't for Alltel whose network is geographically the largest. No single carrier can cover the entire country but while Cingular and Verizon have been focusing their efforts on metro-America Alltel has been focusing their efforts on rural America primarily.
Since the Alltel/Western Wireless merger, the two primary rural carriers have been combined. It's really hard to make a suggestion without at least a clue as to the OPs location, but very generally for the best rural coverage, Alltel is hard to beat. However, as mentioned before, Cingular does provide very good rural coverage in some areas, especially South Florida jumps to mind. The inherent problems with GSM is there are a ton more markets across the United States where GSM (Cingular, T-Mobile) is restricted solely to the 1900 MHz band which isn't near as bad of a problem with CDMA (Alltel, Sprint, VZW). VZW also does decent in some rural areas but you should expect to pay a premium for the same coverage you could get with Alltel. But for the list of licenses to find out who the 850 MHz band carriers are in your area just enter your zip code into www.wirelessadvisor.com and it will show who holds the licenses for that zip.
As far as the phone goes, it's really hard to say unless you specify a particular carrier. Generally, Nokias perform very well if not the best on GSM networks while Motorolas tend to do the best on CDMA networks.