Verizon has generally the best coverage and best customer service, but unfortunately different providers have better coverage in different areas. Just because one provider has the best general coverage does not mean that they have the best coverage for your particular area.
Considering what you have said about where the phone is going to be used, I would recommend going with a multiband phone. Digital phones are great in urban areas, but if your father is out in the country or drives all over the place then his best bet is going to be the old AMPS service. The sound quality sucks, and you don't get all the nice digital features but if it is possible to get a signal at all you'll get it with AMPS.
Here's a list of items I'd consider, in the order that I'd consider them:
1. A multiband phone that supports digital with fallback to AMPS service. He will have the best chance of getting continuous service if he can fall back to the AMPS network when out in the country where digital service is often not available.
2. Make sure the digital service utilizes a lower frequency band. Verizon in SF Bay area (where I live) uses 800 MHz CDMA...AT&T used to use 800 MHz TDMA, but are switching to GSM (which is very spotty right now) because TDMA cannot support high speed data transfer. Other services like T-Mobile and Sprint use the 1900 MHz spectrum. The problem with higher frequency bands is that they don't penetrate buildings as well. Both AT&T and Verizon are by far better in this area specifically because they use lower frequency bands. Verizon edges out AT&T because AT&T is transitioning their old TDMA network to their new GSM network. As they make the transition, the old network will get crappier, and the new network won't be fully rolled out for a while.
3. You said your father travels around a lot. If this is in the same general area, make sure the provider you choose has a good regional roaming plan. If he travels all over the country, make sure the provider has a good national roaming plan (like verizon america's choice or AT&T one rate).
4. Make sure the provider you choose has a decent backout clause so you can test out the phone. Verizon gives you two weeks I believe, and AT&T gives you 30 days. This way you can shop around a bit...try out a phone/service and make sure you get good signal whereever you need it. Another good way to test is to talk to other people with phones...ask them what provider they have and how good they think the service is.
5. Phone selection. Notice I put this last, because the best phone in the world isn't worth crap if you can't get signal or it costs way to much to use it. Phone selection should only be a factor if you have two providers that provide the above criteria and thus are having a hard time choosing which one to go with (even still you should try them both to see if coverage is better with one or the other).