Wingnut, I think you will enjoy your 12 day vacation in Thailand.

For first-time visitor, I suggest you visit BKK and Phuket only, rather than Chiang Mai, BKK and Phuket. Going to 3 cities will be a bit rush and using too much time traveling and moving from hotel to hotel. I would do 4 days in BKK, 5-6 days in Phuket and remaining time in BKK. If you like beaches, there are plenty of things to do in Phuket.

Since you are traveling on your own, fly to Phuket. Samui has nice beaches too, but Phuket offers more variety of daytime and night activities. Beaches in Kho Samet, Pattaya and Jomtien are not as good as the ones in Phuket.

As per your travel date 'collides' with Chinese New Year, it may be wise to book hotel for your last leg in BKK ASAP. Not sure of your actual budget, so can't really make hotel recommendation.