recolonize earth desert with plants : which plants first?
This is a big idea that's gaining momentum in many people's minds across the world.  This is a brief and probably inadequate survey and hopefully other answers / comments will fill out a better picture. 

Most of the plans to reclaim arid regions are not completely hands off.  It seems that the current thinking is that if we waited for microbes and lichen to reclaim arid soil, it would take too long.  Most of them focus on trees.

Trees are fantastic because they can grow in climates that have minimal water once they are established.  They can claim moisture from the air, remove pollution from the air, reduce the ground temperature, sequester carbon, prevent erosion, and make the environment more accommodating to other plants.  

Some estimates are that to curb the expansion of deserts worldwide, 30 billion trees should be planted every year for the next decade.  

The tree one plants varies depending on the place and application, but the selection of the plant is more than just a climatic choice.  Trees are grown in nurseries when their needs for water are most intensive, and then need to be cared for until they are established enough to survive on their own.  

The Green Belt project was the focus of the 2004 Nobel Peace Prize.  Its success in rolling back desertification was because of its understanding of the causes of desertification in many cases as a social effect.*  People harvest the trees, graze the land dry, burn grassland etc.  Green Belt created networks of local people and incentivized them to grow trees, selecting trees which had agricultural and economic value so that they would help the local economy.  

The Great Green Wall project is a successor to this idea.  Attempting to contain the Sahara desert's spread across the continent of Africa.   Their plan is to have a different organization in each country, including automation of sorts to collect water from the air and rain for more continuous support of young trees. 


there are arguments that ultimately the animal ecosystem needs to be involved.