Thanks ruebiracer!
Yeah, I built the chassis as per the manual, so everything is stock (apart from some Yeah Racing hops), and the tires are as you said radials in the front and S-grips in the back. I don't currently have another pair of S-grips, only radials and slicks. But I'll keep your advice in mind when ordering new sets! I could also experiment a bit with the tires I have and see what I can come up with.
As for racing, I'm not currently looking at signing up for the league stuff as I'm very new at the hobby and don't have as much time for practice as I would like to. And I would also need that comp motor to qualify for the racing, anyway. That being said, I'm doing hot lapping and racing for fun in our club, so it's not just driving aimlessly.