Wheels
When it comes to wheels and tyres, most of the decisions are easy. Small is better, up to a point.
Either way, I would plan to run two sets of wheels and tyres. This is to allow testing of different tyres and to have a spare set for track days.
Light Weight
This is good because they are unsprung mass and this the suspension settings can be optimsed with other light-weight components. Obviously, this is a balancing act against the overall strength of the wheel.
Low Rotational Inertia
This is a function of the wheels being light in weight but it is also about the distribution of the weight across the radius of the wheel and is also a function of the overall radius too. Smaller wheels spin faster for a given speed though.
The radius of the tyre (closely linked to radius of the wheel) is also a huge factor in this as it is a very significant part of the overall mass.
Basically, you want to minimise the weight and also keep any weight as close to the wheel centre as possible. This is very desirable as it means they can be stopped (i.e. braked) with much less effort. It also means that they can be turned with much less effort, i.e. the steering effort and feedback is much improved.
Availability
13" wheels are readily available and so are tyres. The speed rating of the tyres needs to be considered though.
Cost
Not a huge factor but, 13" wheels are relatively cheap and a very good set of four tyres can be bought for around £400.