For 2k i'd look at a real tidy Disco for about 1k. Spend the other 1k on suspension and tyres and some good recovery points and recovery gear.

Or the same for a Jimny 1k for an early one a 3" suspension lift, a home made body lift of 2" and some muds and offsets. Trim all the arches and bumper corners and show the landy boys the way! Don't go too big in tyre size though as it kills the gearing as standard.

The only thing i'd say is that a Jimny will sell for more and easier as standard where a disco will be worth reasonable money in either state.
I'd get out with some of your mates and see how their trucks perform, Disco's are great value for money but the little ZUKS will never fail to put a smile on your face.
Even if you started off with a standard truck on mud terrains you become a far better driver off road. If the truck does all the work for you you'll be spoilt and won't learn to read the terrain and pick your lines. I know plenty of people who trial essentially standard SJ's,Vits,Jimny's and regularly show up better equipped trucks. I love SJ's but i'd not choose one over a Jimny. Its essentially an SJ with coils and power steering.

As said get out to your next Pay and Play and see whats working and whats not, bag a passenger ride if you can. Don't rush into buying something then regret it because it wont do what you expect or its not comfortable etc....

Any 4x4 will do what you want with good tyres TBH, as standard they will all have limitations though, it comes down to how extreme you want to go.