Is bigger tyres worth it?

Tires are the first thing everyone goes with for traction.
The suspension is the other half.
Sticking with the tire question, there is a sticky on wheels and tires in that section with (what should be) the wheel size and off sets as well as any spring relocation work done to the car in order to make the tires fit.

On the tire itself, pay attention to the compound of the rubber used on the tire. Also what is legal for you and what is acceptable for use for you personally. Be this for the track and/or the street.

Wider is almost always certainly better.

A 235/60/15 is about a 26” by 8” wide tire.
Even in a drag compound, A sudden mashing or the gas pedal can have this spinning even on a prepped surface.
It’s a balance game between the right foot application on the gas pedal and what the road surface will handle.

It is even more difficult for manual trans guys.