Why gout attacks mostly big toe?
The question has been explored in great depth in the cited paper. Have a look.

Roddy E. Revisiting the pathogenesis of podagra: why does gout target the foot?. Journal of foot and ankle research. 2011 May 13;4(1):13. 

Summary:


Nucleation factors: The site of Gout depends on where the Monosodium Urate (MSU) crystals are likely to form. This process of nucleation depends on a variety of factors. One is temperature, its solubility decreases with temperature and hence the fingers and the toes are more likely sites of MSU precipitation. Further, trauma and pH also affect the nucleation. Repeatedly stubbing a toe makes the first metatarsophalangeal joint (MTPJ) specifically vulnerable.
Cartilage damage and Osteoarthritis(OA).OA sites are correlated with those of higher MSU deposition and cartilage damage (for reasons and evidence, refer to the cited paper). Hence, factors which make MTPJ more susceptible to OA can increase the predilection for MSU deposition. These include "increased concentrations of chondroitin sulfate, degradation of protein-polysaccharide complexes, and epitaxial MSU crystal nucleation and growth on cartilage fragments"


The right sided predilection might be because most people are right-handed, and they might be more likely to injure or stub their right toe.