Any of those towns are fine...
Waltham is more than 15 minutes... but there are more housing options.. for your price range. Town has commuter rail and bus service.
Natick is good... 15 minutes if it is not during rush hour. Rt135 around wellesley is always jammed... but rent is cheaper. Town has commuter rail.
Needham and Newton are both very nice towns... there are lots of apartments. However, with your price range.... your choices may be very limited. Newton has subway and has most mbta services. Needham only has commuter rail.
checkout boston public transportation system.
MBTA.com > Official Website for Greater Boston's Public Transportation System