According to the usual JEE-level order of migratory aptitude in pinacol-type rearrangements (aryl bearing an electron-donating group $>$ phenyl $>$ alkyl, larger alkyl before methyl), which group migrates most readily?

Aryl groups migrate better than alkyl groups because they can bridge the two carbons through a phenonium-type transition state. An electron-donating substituent such as para-OCH${}_3$ stabilises that transition state further, so 4-methoxyphenyl migrates best, followed by phenyl and then the alkyl groups (ethyl before methyl).