It is that easy get a unlocked phone and go. The key is unlocked so you can use any SIM card you decide to get, or possibly many SIM cards. If you only need one card it gets even easier since that will be your phone number, I have been doing this for years and I actually use a different SIM card for different countries. This can be a pain since your number changes. But since you are only going to be in 2 countries maybe a single SIM is good for you.
Another option is to see if your US carrier can supply you a phone. I use verizon and they have a program to supply you a phone for use out of the country. They even have a couple phones that are TRI-Band GSM and CDMA so it works here and there (YEs, they supply a SIM card).

The best part about getting a Quad Band unlocked phone is that you could just move the SIM card frm your current carrier into it. Now you use the same phone all over the world.