Since you'll be using them for a couple of weeks, as Chris posted, best to get three different cards. They won't be expensive and will be much cheaper. If you do only buy 1 sim card, there is the added problem of refilling when in a different country. Not all the prepaid cards permit international roaming.

For Thailand, suggest 1-2Call
Malaysia - Maxis is good
Singapore - Singtel or StarHub

Pretty sure you'll need your passport when making the purchase, very proforma form to complete.

Good luck.