If you don't mind flat sharing then you can find a 2 bed apartment in one of the condos in Tung Chung for around 15K and with a flat share you will be under 8K. If you are looking to save costs then avoid the newer condos - Century Link and Visionary. Check the local Facebook pages - you should find a flat share. I think there are very few 1 Bed apartments except for in Century Link. Am recommending Condos but if you don't mind public estates then you can look at Yat Tung or Fu Tung. Not aware if renting those units is possible and the procedure - better check with an agent or with others on the forum.
There is a bus which goes from that part of Tung Chung to Yat Tung and you can walk from Yat Tung to your work place. You could bike from Tung Chung North side (where all the condos are) to your work if you don't mind the summer sweat.
If you like going to the Island to meet friends then I would recommend Tung Chung or Mui Wo (since it has a ferry). Else you are looking at a very long weekend commute from the other villages to Island/Kowloon