I'm already in Thailand since a month and am planning to do what you describe. Sill at the moment I am more into travelling around - Next month I'm going for Laos and Kambodschia. You definitly don't need a working visa if you work on your own startup code. Best to get a 2 or 3 month tourist visa which you can even renew two times by making a visa run to the border. If you come without a visa you'll get sort of a visa on arrival which used to last one month but seems to be now only 2 weeks! Best go to an cheap island resort with wifi or a nearby restaurant with wifi (where you can stay all day and use the net while ordering a coke every 2 hours).
$10-20 seems pretty high to my standards. I've seen rooms for $5. I would say you get an okay room for $8-14 but you might have higher standards. My current room is $25 and I have wifi by the hotel but I could easily go with less luxery and have wifi from somewhere over the street (often times you get an open wifi signal from next door).
If you have any questions, mail me.