I am traveling to Thailand this August for the first time. I am planning on spending a few days in Bangkok, a few days in Chiang Mai, and then wanted to head down to the beach for a few days. I am deciding between spending time in Phuket, Koh Samui or both. From what I have read, it's a better time of year to spend in Koh Samui, but I am worried about missing the opportunity to visit Phuket.

Any suggestions?

Also, any suggestions for moderately priced places to stay at either location?