Lee,
While R4 Industrial tires would be a logical choice for an average mix of chores, I would think about going with turf tires for the following reasons:
With a tractor the size of the TC40, R4 tires may cause more damage to your turf than you would like. It sounds like this is for a school/field type of use. It is probably part of the job to keep the turf in good shape, and an R4 tire with the weight of a TC40 on it might just tear that turf up a little too much. However, long stretches of straight-line mowing/driving would reduce that, as R4 tires have been known to be rough mainly on turns. But, only you can decide that, so it is probably a good idea to demo one with R4 tires, first.
Also, it sounds like your needs for high traction will be less than low-damage. You can add a set of chains for traction in snow if you choose turf tires.
I hope this helps,
<font color=blue>>></font color=blue>Muhammad
<font color=blue>Forum Master</font color=blue>