You can extend that 60 days by another 30 days just by swinging into Thai Immigration, pay them 1900 baht and presto..you can stay for a total of 3 months (90 days) all up.
when you get here and buy a True sim card. They will usually install it for you if you ask nicely and they are not busy. While you are there top it up with say 500 baht credit. I run 2 cards in my phone. True for local calling and DTAC for mobile internet.