I do quite a bit of offroading and overland style travel with my Toyota Landcruisers and I have always upsized my tires for more ground clearance. It depends on the vehicle but you should be able to go up 1-2" in total diameter and still fit the wheel wells and clear suspension components. For example my 100-series cruiser has 33" tires compared with the 31" stock size.
Unless you are doing a fair amount of offroading or are on roads that require significant clearance to get to your fishing spots I wouldn't bother with upsizing tires and the associated compromises (poorer fuel economy, speedometer calibration, increased wear, etc.).
That's my $0.02!
Cheers,
Mike