Unless you have ultra-specific requirements (which you may have, we don't know any detail about your circuit), integration and mechanical rigidity are the main decision factors for board thickness IMO. If impedances are a stringent concern, just calculate them according to layer spacing whatever thickness you choose.
blueskull made a very good point: absolutely not all 4-layer stackups for a given board thickness are the same, so check that as well. If that really matters in your application.