Shoguns and early discoveries seem to be reasonably reliable.
My mum has a shogun and I've owned a 97 discovery tdi for over 5 years as a daily driver. So I cannot speak for any other models.
With all of these things - you need to know what the problems are.
Most important for you looking at 90's vehicles onwards, is RUST! Wheelarches, sills, BOOT FLOOR (especially in disco's - lift the boot floor carpet before parting with any money!!!!), body hangers and rear crossmember.
Get underneath and have a good poke about. On the plus side, there are lots of replacement panels available, both OEM and aftermarket.
All landrovers rust and if you're looking at getting one, find one that has either had work done already or one that has the least amount to be repaired in future.
If you want to know about landrovers, go and register at landrovernet.com and look at the forums; sticky topics on the different forum sections or post your questions in the relevant subsection.
Your budget would probably stretch to a tidy discovery td5, or an equally tidy shogun (just watch out for hgf on these as they can go but are relatively simple to have done).
Look at plenty of examples until you find a vehicle that feels right.
Anything with a V8 will be hideously expensive to run. If you're thinking of LPG down the line, make sure the engine and fuel injection system is compatible with a reliable LPG system before you lash out on the vehicle.
As for the airbag suspension, common failures are the pneumatic 'spring' and associated pipework/self levelling sensor - this leads to sagging, quite common on rear suspension - a leak in these systems is not terminal, but if left untreated it will kill the pump that supplies pressure for the system. The pump is only meant to run when the suspension needs to be adjusted. When there's a leak it ends up running all the time and burns out. Generally it is the pump that costs the mega-money to replace.
On the other hand, there are retro-fit kits that remove the self levelling suspension system from discovery td5's and rangerovers and replace them with reliable old coil springs if that's of any use.
As for the weight of the vehicles - most landrover varients (disco/defender/rangie etc) come in at about ~2.25 tonnes. Add that to the 3 ton limit for towing inc trailer & vehicle (you'll have to check that). You get the idea. None of these will have any trouble towing the horses or caravan or plenty of other stuff much heavier.
Later landrovers (from the early td5 discovery 2 series) have a lot of electric systems controlling suspension and traction control etc which can go wrong, but are all documented issues that are relatively simple to diagnose.
Mine is a D1 that has abs but no traction control, just good old fashioned hi/lo gears and locking centre differential. If you're looking at diy repairs, the later the model they're slightly less friendly to work on, but you can still do it if you have the tools and the inclination.
I'll say one thing about the diesel engines - the 200/300tdi engines just keep on going (with regular servicing). The TD5 is a more powerful unit, and while it is reliable, it is less so than the tdi by many accounts, but don't let that put you off - in no way is it a bad engine, you just need to pay more attention to the servicing & diagnostics as it's all ecu.
V8's have their own troubles (even though they sound great).
Last thing: VED. On a 2001 TD5 it will cost you ~£400 to tax for 12 months. And older TDI will be about half of that. I suppose the larger figure will apply to later rangerovers etc.