What did the Whig Party believe in?

Economic protectionism, and that Andrew Jackson was a menace.
The Whig party was founded in 1833, as a reaction to Andrew Jackson, to credibly oppose him in the 1834 election. (They failed.) Jackson was an outsider who, in the Whigs’ view, hijacked the Democratic party (splitting it off from and replacing the Democratic Republican party, which had been around since Jefferson first ran for President)..
The first six presidents were upper-class planters and/or attorneys from Virginia, or were Adamses from Boston, but were all from the same social class. The first five were signatories of either the or the Constitution (Founding Fathers) and the sixth, John Quincy Adams, was the son of a previous president.
Andrew Jackson didn’t belong to this little club. He didn’t come from old money, his wife had a mildly scandalous background, and he was a flashy war hero who milked his legend to rise through the political ranks of Tennessee, at the time considered something less than a real state. He was swept into office in the 1828 election and his opponents, outraged that a low-born populist could get elected without their permission, formed a political party specifically to oppose him. They were the Whigs.
“Whig” meant “anti-tyrant.” The term had been around in America since the Revolution. They favored a strong congress and a weak presidency, protectionism for American business, and whatever would dethrone Jackson and the Democrats. They opposed Masonic influence.
During their 21 years of existence, they fielded four presidents: William Henry Harrison,Zachary Taylor (both war heroes like Jackson, interestingly), John Tyler (expelled from the party when he succeeded Harrison) and Millard Fillmore. Henry Clay and Daniel Webster were party leaders. By 1854 the remnants of the party were absorbed into the Republican party.