Skip Verizon. If you want web, try the mytouch 3g and the iphone, Tmobile and ATT respectively. G1 from tmobile is also a choice if you want a hardware keyboard. Blackberry's might work for you but honestly I know very little about those.
Android is playing catch up to the iphone dev/userbase. There are more devs, users, and programs for the iphone. Period. I'm a G1 owner and love android, but seriously the Iphone has stuff we don't, and we have stuff they don't. Both devices have their unique "killer apps". (there's enough of this us vs them garbage on the internet between the two already, there's no need to start more).
They're both great phone OS's and are the only ones that are really relevant at the moment. Blackberry is also holding strong. (again I don't know much about BB). WinMo, Symbian are outdated, and the Pre doesn't have the apps to back up the OS yet.
I used to sell phones and honestly, do the research, compare the rate plans between the companies, then go into a store and play with the phones, what ever you like usability wise / rate plan wise go for. There is no "BEST PHONE" on the market and different things work for different people. I'm not going to try and sway you into a phone that isn't a good fit for you just because I have a pro android or iphone agenda.
Heck you might like the verizon rate plans and phones even though I can't stand them. Different strokes for different folks. I have friends who love verizon because everyone and their mom has verizon so they have unlimited calling.
I use android daily and I play with iphones often, and really it's a matter of user preference, they both provide a good user experience. Pick which you find more usable rather than what others push on you or what ever is the "flavor of the month".
As for coverage, where are you using the phone? You mentioned traveling, are you in country or traveling abroad? I'm sure ATT and Verizon both have coverage maps, heck we had ATT coverage maps online 4 years ago when I was still working for them. I'd be willing to help dig up coverage maps for all the companies you are interest in.
Ltown clearly wants you to go android and tmobile, I'm sure the ATT salesmen on here will want you to go towards the iphone, but really, it's a matter of finding what device and service is right for you.
Sorry if I've stepped on anyone's toes / pissed you off / whatever. I sat here rereading the post preview for a good 10 minutes trying to work this post out so it wouldn't blow out into a flamewar and at the same time trying to be unbiased and informative. I don't feel it's right to push him into a phone and service that may not be the right fit for him.
)