I travel to SE Asia fairly often and in two weeks I'm heading back for a trip to Myanmar. I'd like to have a mobile phone this time around so that I can call guesthouses to book rooms, keep in touch with other travelers, etc...
In the USA we use a different mobile phone system, so my current phone won't work in Myanmar. I read somewhere that I need an unlocked GSM mobile phone and can just buy sim card there to use for it. Do I have that right? If so, is it cheaper to buy an unlocked phone there?
That is correct. You need to buy an unlocked GSM phone. It will work in most countries of Asia, Japan and Korea being the only exceptions I am aware of. If the phone is unlocked, you can just change SIMS to use the local network.
You don't mention where you plan to buy the phone but I figure that in the more open countries like Thailand, SG, Ph and Malaysia you can get cheap cellphones.
A basic China brand cellphone for sending text messages and calling can be as low as $20. A basic Nokia cellphone might be about $25. Many of these phones are sold unlocked but it is possible that a telco will sell a locked version of the phone. So before you buy, make sure the phone is unlocked.
I've come across stories about the weird situation in Myanmar where you can buy a SIM but you can't reload it.