Sorry for the slow response but I've been offline for a while.
1- I would recommend HH over Cha Am. The latter is rather a Cinderella & the few foreigners who live there usually commute to HH for shopping, eating, etc. However, it would be cheaper than HH!
2- Finding enployment as a teacher isn't too hard, especially with government schools. The problem is the work permit. However, if you send your CV to every school in the neighbourhood, who knows what will turn up?
3- You might have a problem finding somewhere comfortable in the price range you mentioned. HH is a tourist town & so it is pricier than neighbouring towns.
Hope this helps!