Rear tyre is just a 175/65 R15, doesn't need anything fancy, the original Yokohama Bu-Earth is a good tyre and works well, some of us over here are using cross-climate tyres but cold weather isn't likely to be a big issue for you! Pretty much anything that isn't too asymmetric will do the job, it's the front tyres that limit the grip as a rule.
Best/latest/easiest rear wheel alignment I've come up with is to get the wheel slightly forward of where it wants to be (belt a bit over slack) with the spindle hand tight giving a bit of resistance to adjustment, then draw one side back till it is same gap each side from the forward edge of the outer adjustment plate to the middle of the cut away in the swing arm. I use a caliper for this and just compare the two sides till they are the same - the measurement doesn't matter. Then draw back evenly on both adjusters till the belt is tight; about a 45 degree twist in the middle of the lower run with weight on the wheel then nip up the spindle solidly.
Quick and rough sketch;
I did a fair bit of measuring on my swingarm to convince myself that this gets the spindle square across the back and parallel to the axis of the swingarm bearings and it seems to work.
