This is my opinion based on my findings travelling around the traps.......
Well serviced vehicle.
Good tyres. No need for new Mud terrain or fancy tyres. As long as they are a good construction tyre with still a good amount of tread they will be fine.
Tyre repair kit. (I also take a spare tube and tyre levers but thats being cautious and ive never had to use them..yet)
12v compressor.
Good shockys, as in not worn out. No need to go and buy expensive or even new ones if the ones in your 4wd are still fine.
A good snatch strap or two.
Recovery points.
As for spares this will vary depending on the vehicle and its age etc. I carry belts, hoses and few bits and bobs specific to my potential needs. Oils, some fluids etc once again specific to my vehicle and its age.
I also carry a good but compact tool kit. Things like a small collection of electrical bits and pieces, some magyver type nuts and bolts, wire, cable ties, tapes, metal mend, epoxy etc. Lots of lists and things on the net about this type of thing. Personally some lists are far too comprehensive but until your stuck in the middle of no where and need something you dont have then the list doesnt seem so comprehensive LOL
In a group people may want to share the load as such but I like to be as self contained as I can because I wont always be with a group.
The biggest mistake I see people making is that they install a heap of new goodies for a trip and dont test them prior to the trip. You know the guy that runs a 12v socket to the rear of his 4wd to run his brand new fridge, gets out in the desert and suddenly the fridge keeps cutting out because his system is not adequate. Or the chap that has the brand new 4wd with every conceivable bolt on accessories but has never driven off road let alone slept in his swag/tent out in the elements for a decent period of time and continually whinges and moans because his air lines on his 'lockers' keep blowing off.
I much prefer to see people put their hand up and say I am inexperienced and be open to allowing others give you tips and hints and encouragement along the way (we are all always learning no matter how experienced) rather than having all the gear and no idea. We are all potentially going to get stuck every now and then or have a few goes at a soft dune, there is no shame in that its a part of the fun. And in most cases it happens because no one wants to be the cowboy that hits every big dune at 100mph so we generally try to get up over obstacles with the least amount of mayhem as possible so it catches you out. As a trip like this goes on everyone gets the hang of what will be for some, the first time they have driven over a dune, so a good attitude and sense of humour is usually more important than $50k's worth of bolt on gear.
Nice to have in my opinion is a way of showering with hot water from the 4wd, good drawers for storing all your gear, fridge/freezer and enough battery power to run it in between drive days, a decent led lighting system, sat phone, gps system, a good water and fuel storage solution. Maxtrax type things, long handle shovel, exhaust jack (i have one of these stupid things, I might take it to the desert and see if it can get some use finally!). Winch, straps of various lengths, shackles, snatch blocks, sand trap etc all nice to have but for most not needed. Some of us will have all that gear so thats all that matters.
Sure a lot of us will have all these things but they are not necessarily essential, especially if your with a group. For every fancy gadget on the market there is a poor mans way of doing things (im a poor man so I know LOL)
There is no doubt a lot more and everyones opinion will vary so thats a start. But don't over think things and get overwhelmed by the thought of 'crossing the simpson desert' its not as daunting as it used to be and there is so much information out there to scramble your brain when trying to prepare for a trip like this. Keep it simple. Reliability and driving to the conditions is where its at
Peoples personal levels of comfort beyond those two things is going to vary a lot!
Just while I think of it, it might be worth mentioning what people are taking that can help the group but its not necessary for the whole group to carry. As an example recovery gear.
I seriously doubt we will need anything more than the odd gentle snatch but I have a winch, tree straps, equaliser straps, various extensions, snatch blocks, shackles and snatch straps so no one really needs to stress too much about buying too much recovery gear besides a snatch strap. I carry my recovery kit anytime I go on a big trip regardless of where it is because I have been caught out. Sometimes something as innocent as driving off the side of the road can end in a recovery.........but no need to tell stories LOL
Should be a good thread this one