Snatch not really possible in this situation
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For self recovery you can get really lucky and be stuck within reach of a tree or bush and get yourself out. When other vehicles are involved it's much more controlled and safer as well as less stress on the vehicles.
Desert basics is a shovel, jack and wooden board to place under the jack. The rest of the recovery equipment is personal preference. From what I've seen the maxtrax work well and a snatch strap or tow rope needs to be on hand in case of break down and you need to pull the other car out, what I really want to get again is those balloon jack those are so easy and quick to use and kifts you right up.