Air recycling system(CO₂-->O₂) or (CO₂-->fuel)?
This is quite a hot topic at the moment - the current buzz-phrase is power to gas.

There are quite a few conference papers and technical papers, and at least one dedicated conference, for it.

And it's too soon for there to be a known "best" process.

Audi and others are using a modified Sabatier process.

$$\ce{CO2 + 4 H2 -&gt; CH4 + 2 H2O }$$

Others are looking at a modified Fischer-Tropsch process.

$$\ce{(2n +1) H2  +  n CO -&gt; C_{n} H_{2n +2}  +  n H2O}$$

(image courtesy of the RWE power to Gas Project)

Essentially, you've got to prise the Oxygen off the Carbon, which is an energy-intensive process; and then attach the Hydrogen, which is not. But the Hydrogen typically comes from electrolysis of water, which is energy-intensive.

Not only are the processes being prototyped high-energy, but they're high-exergy too, requiring very high heat and / or electricity.

So it's unlikely that this is a better option than using solar power for solar-thermal or photovoltaics, unless the application is long-distance travel, which would require an energy source with a very high energy density. In which case, there are several renewable-fuel synthesisers being prototyped at the moment, but it's too early to tell which is the best.