We have a quinny buzz, because a friend had finished with it, so it was going free. It works okay. I've taken it on buses, trains, and in loads of cars. It fits a car seat.
I would think carefully about whether you need off road ability really. The buzz is a kind of off road compromise which is okay for me, you can go over the odd root or step (or recently I took on the local bmx jumps). For things like parks or wide woodland paths, you don't need an off road thing at all, it is only rooty singletrack or rocks where the smaller wheels will get stuck. I don't think the big wheels are a massive advantage in town. I take ours on singletracks because we have a bunch of nice walks near us where it makes sense to nip through shortcuts, but that is the only reason it is at all useful having the wheels as far as I can tell. Oh and also going down our road - which is an 18th century stone road, made out of massive lumps of gritstone, kind of like giant cobblestones, smaller wheels can get stuck in them. Other than that, we live in a very hilly town in Derbyshire, with hilly parks and woods, walk an awful lot (no car) and I doubt we really need it other than for being nice on our road.
The downside of big wheels and all that is that things are bigger and heavier, and you often need to take wheels off to put them in a car boot. For us, 90% of the use is pushing around, as we live right near town so it isn't a big problem, but it would be a bugger if you had a smaller car and drove much, or were pushed for space at home and needed to fold it often.
Oh, on the car seat thing, I think our car seat (maxi cosi one) can click into some kind of clicky base, but also works fine with seatbelts in taxis or other people's cars, and also clips onto the pram base, which is good - we use it way more than the carry cot add on for the quinny (I wouldn't bother buying that to be honest). So you get the best of both worlds.
If you do get a big pneumatic wheeled one, Schwalbe sell decent bike tyres & tubes in those sizes that don't get punctures all the time (I think they are called 'City Jet').
We also have a sling, which is often a magic sleep machine, so it is worth getting for that alone. We have a Moby Wrap, which is kind of a bit fiddly first time you use it, but seems very comfy, and very unlikely to give you a bad back. To be honest, I think people who don't have slings are more likely to end up with bad backs as they spend much more time carrying babies in their arms, which is more achey making. The sling or similar is also the only thing you can use to go on a decent proper walk in the country, unless you like lugging massive buggies over stiles, up rock steps etc. or want to limit yourself to sustrans style tracks.
Also, don't spend too much on anything, and buy things second hand if at all possible, even if you have rich grandparents. Some babies just don't get on with some stuff, and you'll end up selling things off / chucking them out (like our baby doesn't get on with the £100 Quinny carry cot), better to get 2nd hand so as not to have a big financial hit. NCT do 'nearly new sales', which are like cross between a big jumble sale and a fight* - if you turn up super early to them, you can get stuff very cheap. Our local one lets pregnant women in 15 minutes early too.
[three wheelers] Often very unstable when lifting over kerbs though.
Really? I can't see that being any hassle - you're on the two back wheels going up or down a kerb, same as any pram. How can it be less stable?
*at our last one locally it apparently really did kick off between two people wanting to buy the same fancy pushchair!