Pointers please towards a gentle intro to green laning and off roading.

Bf goodrich urban terrain. I use them on the farm and they work on wet grass, which is about the most serious of tests for any tyres. On road they are awesome.

Having read the tyre wiki (which is really good) I am aware of the need to have all 5 tyres the same and not tyres with a rotational direction (as they can't be rotated except on one side - and the spare would only suit one side!). That would exclude the BFGUs unless I am looking at the wrong model of tyre - there are so many on each site!
The general Grabber AT3 looks like it would fit the bill.
So is there any advantage to getting a wider tyre and I don't want it catching on my unmodified wheel arches.
I don't want to kick off a huge tyre debate, this is just me going mainly on the road and occasional fields and lanes.
Thanks.

The bfgs are asymmetrical not directional. There is an inside and outside which needs to be observed when mounting the wheels but once on wheels they can be rotated as normal. Mine are on their second rotation now.

Grabber AT3 are a good bet or Yokoharma Geolanda A/T-S.(go-12) not much point going wider but possibly taller to gain clearance under the diff's.

If I went for Grabber AT3, which seem to be available in all sizes and profiles, how do I go taller without wheel arch issues? What profile would I look for on a 205 to 225 tyre on a 15" wheel with no mods on the car please?

205/75/15 or even 215/75/15 will go on a standard jim without any mods. 215/75 is the limit though and if you have the later type bumper they may just touch the corner on half lock. Just need to trim about an inch of the bumper. No problem with the arches.