Tyres are the single most important part of an off-road vehicle.
Choosing a suitable tyre is not as easy as it used to be, the main points to look out for are:

Speed, Budget, Load, Road surfaces, looks.

Speed is not such a concern to the regular person but if you regularly do high speeds (110+) with a heavy vehicle then you must study the tyre specifications carefully. Usually as the speed rating increased the load rating decreases.

Crossply tyres are significantly cheaper than radials, they usually have a low speed rating, a high load rating and are extremely tough. They do not have a very good expected mileage and are the worst on tar.
These tyres are used mainly for slow hard work :- serious off roading with heavy loads, largely an industrial type tyre.

Generally, the more aggressive the tyre tread, the worse the on-road handling gets and the better the off-road handling gets. You must descried what percentage on and off roading you are going to do and what level of of off roading it will be.

Sand generally requires a wider, smoother tread with as few knobs and bumps as possible.
Mud on the other hand wants lots of knobs and lots of open spaces between. Modern tyre design concentrates on a good self-cleaning action.