Iirc McKinley was the only president to ever write a major tariff bill (though to be clear, he did so prior to serving as president), and as president signed into law a major bill that raised tariffs, so he seems like a reasonable choice for most protectionist. JQA, Buchanan, Lincoln and Hoover also signed major tariff rate increases, but it wasn't the major domestic policy initiative for any of them (and Hoover had actually hoped to decrease tariffs). That does leave Harding, who signed a major increase in tariffs in 1922, but in his career he was never as associated with the tariff as McKinley was.
For free trade, FDR probably had the biggest impact in establishing the free trade era, although Truman and Wilson (by re-establishing the income tax) were also quite important in that regard. 19th century Democrats were also very pro-free trade, so you could reasonably argue for Polk or Pierce, who both signed tariff reductions. You could also argue for Clinton, who held office at a time of low tariffs and further increased international trade by pushing through NAFTA and granted permanent normal trade relations with China.
Trade protectionism was a cornerstone of Lincoln's economic philosophy, and his administration marked the beginning of a period in which the American System became firmly established as the dominant economic policy for the next several decades.
