You say you like the 'idea' of trying some off-roading, implying you are a novice.
In which case I DO NOT reccomend full Mud Terrains.
Full muds have loads of 'bite' in the slimy stuff, and for a newbie, they will get you a long way into trouble before you are aware of it.
I always advise starting out on AT's, becouse they are a better all-round tyre, to begin with; they are quieter, more stable, and have a lower rolling resistance which is better for ecconomy on the road, while 'off-road' they can actually offer MORE grip than a mud on surfaces which aren't 'muddy'.... like hard packed clay-trails, gravel or rock, particularly slimy wet rock!
BUT for a newbie, in the slimy stuff, you'll loose traction an awful lot earlier than you would on muds, which isn't a bad thing.... means you dont get as far into an awkward situation before you need to employ a little recovery activity (perhaps as simple as backing up, if not getting some-one to give you a yank with a rope!)
Does a few things; first off it teaches you how a car behaves near, at and beyond the limit of traction, and hopefully in situations where if you get it completely wrong, you aren't going to be in any seriouse trouble.
Next, it teaches you to 'drive for traction'; ie relying on your driving to read the terrain and pick you paths to find the most traction, drive for momentum, so you keep the car moving, reducing the need for as much traction, etc.....
Which develops your skill, and a half competant driver on AT's will usually get a lot further than a numpty on muds......
Meaning you may never NEED full muds, or if you do decide you want them, you'll get a heck of a lot further on them, and hopefully have the nouse to know what you are doing, and not let them drag you into situations you cant handle.
Proof of the pudding, I've lost count of the muber of times, Ive taken a tame-tyred Rover through sticky stuff, where people with much more capable kitted rovers with much more capable rubber have struggled; but the one that I remember most fondly was in Wales, leading a group of newbies, following a group of more ardent 'enthusiasts'.
In my group I had a little Seires III SWB Diesel, that had been restored on a shoe-string by a primary school teacher as his summer 'project' and having built it, decided he 'ought' to take it 'off-road' just to say he had... he was incredibly nervouse, though, becouse on his budget, the only tyres he could afford were 'milk-float' remoulds.... ie; they didn't so much have 'tread' as half a dozen zig-zag indentations running round them!
Drew up to a mud-hole, which had cought the group we were following; a Toyota, had got seriousely stuck, and claimed his electronic diff-lock had gone awry, though he was chucking mud off all four tyres, so I didn't give that claim much credance, and the lifted, MT equipped 90 tryng to haul him out was chucking as much muck, and slewing around on the rope, on the 'firm ground' beyond'.
Having only just strugled through the pit himself, and after extricating the Toymota, 90 Driver suggested he'd leave his rope on for when I went through, as I'd 'Never' manage it on my Wranglers......... I did! (without diff-lock, as well, just to silence the Toymota pilot!)
And so did the Anxiouse Annie in the 88!
He had wanted me to rope him up and pull him through, before he even began, but, infront of an assembled group of blokes with kitted and Mudded Motas, swinging strops and shackles, waiting for the presumed inevitable, shaking thier heads at his chosen wheel-wear....... I convinced him to give it a go; second low box, third throttle, a couple of cars lengths to get some momentum, then let it chugg through, 'hands-off'.....
NEVER seen a bloke so exited! He came out the other side, whooping with joy, like a kid at a fairground, shaking his head, becouse he couldn't believe his milkfloat tyre shod old 'shed' had done this hole that had cought so many 'properly' prepped motas!
Anyway!
As for specific tyres; Arghumph! answered this one SO many times, difficult to know where to begin. every-one has so many different ideas about what is important in a tyre.
OK; BFG's have for a long while been the 'Bench-Mark' by which all others are judged.
Their AT is a very good all-terrain tyre, the Track-Edge 'AT' was an AT with a bit extra for the gloopy bits, while the MT was the standard for slimy stuff.
They wear well, have pretty good road manners, & for the tread type, work well in thier intended off-road surfaces, and cost a heck of a lot of money!
My preffered tyre was the Goodyear Wrangler, which was 'almost' as capable an all-terrain as the BFG AT. It lost out a tad in sticky situations, but lasted longer on tarmac and was a tad cheaper.
The Pirelli Scorpion, was another good alternative, being slightly better off-road, and cheaper than a Track-Edge, though not quite as good in really thick gloop.
NOW, trouble is, that in the last ten years, tyres have 'diverged' and what were being sold as All-Terains are now being sold as 'Muds' or semi-muds, and what are being sold as AT's are often street tyres with a section of slightly more open tread patern!
These are often titled AT/2's, as with the new Wranglers or the General Grabbers.
It is, I guess a trend started by people that have pretty much road only 4x4's that they have the 'idea' they'd want to be able to use on something other than tarmac, or who want something a bit more rugged than a road tyre to cope with dragging a horse box or caravan accross a field.
I have Wrangler AT/2's on my Rangie, becouse that was what was on it when I bought it. for the heck of it, I thought I'd see just how capable they were in the slime, green-laning down on the plain in the rian......
Now, I was quite pleasantly surprised by them. For what was some mild to mildly challenging 'laning', they coped remarkeably well.... and trundling about with a bunch of other nutters, coped with everything I chucked them at....
There were a couple of placed they struggled, that I know that my muds would have 'eaten', but I drove through them, and never needed recovery....
Conclusion: Well, for a newbie, probably as good a starting place as any.
So, depending on what you have at the moment, if you are renewing a pair of tyres, if what you already have are AT/2's or similar, rather than pure road rubber; yeah, stick with them, and go for it.
when you have done some playing, and found the limits of the tyre and are feeling that they are really the main thing holding you back, then think about the other rims, and whether to go AT or full mud.
If what you have is strictly a road tyre, and want a full set of something more useful for off-roading; then I'd say get a set of 'propper' ATs on your spare rims.
They should be good enough for almost anything you'd want to tackle, if you learn to drive for traction, and you could easily see out their life without wanting to change them again for something more rugged.
But if you DO, you can put the dedicated muds onto the old road rims, and swap them over, pushing the AT's into road survice, as they still work well there.
Specific tyres to suggest for an AT, well after the BFG, I have to suggest the Avon Range-Master.
It's an open patern, genuine AT not an AT/2, with a tread pattern pretty similar to the Wrangler or BFG, and known to work well. Its also a brand new carcass tyre, not a remould, and one with a reputation for long life curtecy of a slightly harder rubber compound, which does make them a little less grippy on damper surfaces, but not so much as to worry about, and certainly an awful lot better than a remould and DEFINITELY more reassuring than a full mud!
Best thing about these tyres though is the price; they are currently in Craddocks for less than many remoulds, and about 1/3 the price of equivilent BFG, and 1/2 the price of almost any other alternative! Incredibly good VFM at the mo.
In fact, a full set on your spare rims, may be little more than a pair to make up the set of street tyres; and as they would work well on road as off it, and last, might be worth going that way and fitting them full time, and leaving the road rims in the garage until you have a better use for them.