Your best bet would be to stick with the standard wheel size (or close to it), and find a more aggressive tread pattern.
Take a look at my Panda 4x4:
You might be best searching for ATV or quad bike tyres, as opposed to searching for car tyres, if you search 4x4 tyres you will only find bigger.
The previous comments have hit the nail on the head... sticking bigger tyres on will not be that easy...
You will loose road handling and decrease your turning circle for starters. You need to raise the suspension (back is easy with brackets), but this will throw out the propshaft lengths among other things.
Basically, unlike with a Land Rover, the bits you will need are not available off-the-shelf, you need to custom make loads of parts, or have a bottomless wallet and get someone else to do it.
Or you could bodge it, and spend all your time trying to fix broken bits.