Hello Dave, welcome aboard.
I've had my car seven years and have driven 148,000 miles in it from new. In that time I've had the opportunity to try different tyres. I've also driven a fair amount of other people's GT86's too.
I kept the Primacy tyre for the first 25,000 miles or so. I think it's good to learn the balance of the car with this tyre. You can play with it at low speeds and it's a lot of fun, bringing out the playful nature of what is an excellent and well balanced chassis. The Primacy tyre is also fantastic fun on track if you so wish. After about 4 laps they go off, but stay consistent and you can just slide and drift the car all day. They last really well too.
That said, they aren't the most progressive tyre and it can be a bit tricky in the wet. Yes in low temperatures in greasy conditions they can prove tricky, though that is true of any tyre.
Everyone will tell you to fit Michelin Pilot 4 tyres. Whilst they are a great tyre, they take away from the playfulness of the chassis. They are a a great choice if you are not a confident or experienced driver as for the most part they will totally tame the car and you'll feel more confident. I have these on my car because I sprint my car and they are the most competitive tyre in class, giving around a 1.5-2 second advantage on a sprint lap. Yes, at high speeds you can still slide the car and have fun, providing you are committed, but the speeds at which you do this mean that you will not really be able to do so on the public road.
The PS4 is great in the wet too. In fact they are utterly brilliant in the wet, a point I have underlined whenever it is wet in the Toyota Sprint Series, which will see all of us running them at the top of the leaderboard.
I like the PS4, it's a great tyre. But, you have to push it to have fun on the road.
Another really good choice is the Yokohama Advan Sport V105. I have gone through 5 sets of these and would have carried on with them were it not for them not being competitive in the sprint series I compete in. They are perhaps the best balance between grip and playfullness for the GT86. They are more progressive than the Primacy but not as grippy as the PS4. This means you can still have fun drifting a roundabout or on a decent B-road blast. They do really well on track too and you can slide the car around just as well as the Primacy.
If I wasn't competing in the sprint series I would run a V105 instead of a PS4. It makes the car far more fun to drive.
The other point to note is that I use stock 215/45/17 sizes albeit on a forged lightweight 17x8 wheel. If you like to play with the chassis do not make the mistake putting on wider tyres. All it does is detract from the fun and add unsprung weight.