That phone is unlocked so you won't have any problem with GSM. The thing is that basicly all flip phones keitai are triband: that means that if you travel a lot, and go in rural areas you probably won't have signal (because in that areas they use the 850Mhz band, which keitais don't have).
About 3G .... I don't know. You shouldn't have any problem with an unlocked docomo phone, but I'll let the other forum users to confirm that. ... same goes with your carrier, I have no idea how well it would work with Verizon Wireless. If it's a normal SIM card, in theory it should work fine.
Other model you can be interested in is the F-02D, which is the most high-end unlocked keitai flip phone (it has 1,2Ghz processor)