It sounds like you are going to be using the turbo exclusively for the next few months. Now it's not essential to use a specific tyre for the turbo. As you are a bit apprehensive of swopping the tyre, I would just put the bike on the turbo and ride it. If you are going to start mixing indoor/outdoor rides you would have to swop tyre before each change, which would be a hassle,( but good practice). I would take the option of using road tyre on a turbo, rather then turbo tyres on the road.
When you get into serious training, then a dedicated back wheel or even a complete bike for the trainer would be the way to go.
But whatever, you decide, don't wait for a puncture out on the road. Do lots of practice in the comfort of a warm house.