If you're able to commit to a certain length of time/frequency, "the cheapest private" cost I've found is @ Chacrit Muay Thai in Bangkok (6000 baht for 15 sessions which comes out to 400 baht/per). In fact, they ONLY do privates. It's kind of a unique situation as Muay Thai camps go, as you basically just show up and work with a trainer. They don't run classes. There are usually several trainers on hand and once you work with one, you're pretty sure to work with the same one as long as you let them know when you're coming next. Really good spot for a beginner for sure!!