The starter is part of the ballast
So it goes with the ballast.
Changing from T12 to T8 is a good thing to do. You have to change the ballast.
T8 ballasts are almost universally electronic ballasts, do not use starters, and use one of two wiring schemes.
Old-style ballasts that use starters use quite a different wiring scheme.
Your new ballast includes a wiring diagram, either on the label or its instructions/data sheet. You will need to convert to this new wiring scheme. It will not involve starters. So there is no reason to be shopping for starters, unless (amazingly) your T8 ballast requires one, in which case you'll need to use the starter it proscribes.
Choices of ballast type
Since a starter based lamp does use preheats, that means your lampholders will be 2-wire (non-shorting). That means you can use any modern T8 ballast (which matches your bulbs): instant-start, rapid-start or programmed-start.
- Instant-start ballasts don't use the preheaters, and strike the arc with sheer brute force: a big voltage spike. This is hard on the tube, and will necessitate more frequent tube changes. (that's relevant if the tube is difficult to change).
- Rapid-start ballasts do the same thing starters do; they use the pre-heater filaments before striking the arc, to ease wear and tear on the tubes.
- Programmed-start ballasts preheat intelligently, actively monitoring tube conditions until the ideal arc strike. These are far easiest on the tube; the tubes can even outlast LEDs! However, this patient preheating can annoy; for instance at -20C they can take 4-5 seconds to start.
Keep in mind T8 ballasts won't feel traditional; they won't flicker at 100Hz, won't flash on and off at times, and won't perform horribly in the cold. Also, the T8 tubes will have good clean >80 CRI light.