The best coverage is through CDMA carriers like Verizon and Sprint. The easiest and very cheap way to get this coverage on prepaid is through Net10. All you get is talk and text though, but it doesn't sound like you need data anyway. It is 10 cents per minute and you can roam on pretty much any CDMA carrier in the US. The phones are essentially free as well if you get a cheap one. The only thing to remember is that you have to find a hole in the GSM coverage since that is their default. The zip code of 29685 is a CDMA only area so it will bring up the phones for that series. You don't have to ship to that zip code or activate the phone with a number from that zip either, just input the zip when shopping.
Now personally I dislike Net10, but for a foreigner coming over it is probably the most hassle free way to get the best coverage and decent rates.
The only problem with Sprint and prepaid carriers that use their network is that their coverage is pretty limited, especially in rural areas. If you have a postpaid (i.e. not prepaid) Sprint account, you have roaming privileges on Verizon, so that's not something you'd really notice. However most prepaid phones that operate on Sprint (especially non-Sprint branded, like Virgin Mobile) only allow access directly to Sprint's network, not Verizon's, resulting in tremendously decreased coverage in non-urban areas. Sprint operates a 1900 Mhz only network, which has much less limited range than Verizon and AT&T who own substantial licenses in the 850 Mhz spectrum.
In short, I'd stick with Verizon or AT&T if you want the best coverage. Depending on the part of the country you are in, one or the other may be superior, but both are good bets.
Also, there's nothing inherently better about CDMA as far as range goes. If Verizon (a CDMA carrier) has 850 Mhz spectrum in your area and AT&T (GSM) doesn't, yes, you will have much better coverage on Verizon. In some states where the situation is flipped, AT&T offers the better service. Both have a roughly equivalent number of towers and coverage area.
One benefit that CDMA has over GSM is it's much easier to implement 3G, which is why you see all the ads of Verizon touting their 3G coverage over AT&T's. GSM/WCDMA 3G can offer much faster speeds if equipped to do so, though. In any event, all this applies to data coverage, so it wouldn't affect the OP.
I tend to see AT&T's prepaid phones in more stores then Verizon, but again, either will be a good choice.