If all 3 call, go with the TA appointment. You’ll get the city pension and if you were to transfer to another city job or TA title, your time of service carries over. Also, you need to be TA to work in Staten Island or the Casey Stengel, Jamaica or Queens Village depots in Queens.
With OA or TA, you will be able to work out of any depot in Brooklyn, Manhattan and the Bronx, subject to your seniority and excluding the TA only locations mentioned above.
If you’re thinking of moving up to dispatcher, then you can only work in your territory. Meaning if you’re TA, that’s only Brooklyn, Staten Island and Queens (again Stengel, Jamaica and QV) OA is only Manhattan and The Bronx. Only way an OA dispatcher can work in Brooklyn is at the Command Center. Superintendent and above, you’re going wherever they need you.