you will have more grip when you are acceleating, you brake turn and slowly apply power to push you through the corner, you will always understeer when pushing if you are not driving the car, ie on the gas.
but yes the tyres need to be the same coumpond front to rear to get the best, and dont think of the front and rear, they both affect each other, too much grip on the rear and you will understeer, to much on the front and over steer, simple, its all about balance