Tyres

There are two main issues here

The material the tyres are made from
The decision to have a tread pattern or not.

Slick or treaded tyres?

Slick tyres offer the best grip in dry conditions as they give the maximum contact area between tyre and road.
The softer the tyre the more grip you will have, but it is possible to wear out a set in one race if you drive hard
Tread pattern is important if it is wet. The purpose of a tread is to remove the water from beneath the tyre. Without this the tyre will actually sit on a layer of water rather than the road, giving very little grip. This will have the obvious consequences or loss of control and you will not be able to use anything like full power.
The use of treaded tyres which remove water effectively could well give you a winning advantage on a damp or wet circuit.

Material?
The tyres supplied with your kit of parts are made from foam rubber. You can improve on them considerably. Here are couple of ways to do it
Rubber is much better compound than the foam, and might be a wise investment for some of your money in purchasing rubber tyres, they are available with and without tread.
Another way is to use its silicone sealant which is available from most DIY stores and builders merchants. This is very soft and provides fantastic grip. It can be spread evenly over the surface of existing tyres. You could even make a tread pattern surface to roll your tyre on when the sealant is still soft.

Turn up with both to race day. Score points for the planning involved even if you don't need to use different tyre types on the day.