If running on pavement a lot maybe an aggressively treaded tire, like a full scale 4x4 tire. The larger blocks should last longer on pavement compared to a smaller block or pin type, a little better control with less squirming too. Something like the old Proline Dirt Hawg (which may not be available anymore):



Another option, you mentioned short grass, as you've undoubtedly seen 1/10 buggies (my presumption on the 1/10 scale) aren't great in grass. On many buggies you can mount 1/10 stadium truck rims and tires. The bigger tires can really help. Just remember to gear down, smaller pinion gear on the motor, to compensate for the taller tire / longer roll out.

Front tires are typically less critical for this type of fun, but matching sets are usually a good thing if budget allows. Mounting front stadium truck wheels might be more difficult though.