If you're looking for an authoritative guide to the ideology of the early Republican Party, pick up Eric Foner's Free Soil, Free Labor, Free Men Essentially, what Foner argues is that the early Republican Party coalesced around not just a moral dislike of slavery but a commitment to 'free labor' - that men (and it was almost always men) should have the right to control and manage their own labour and benefit from it. You might find that an interesting read.

To answer your question, I'd say firstly that the early Republican Party united around antislavery rather than any commitment to fiscal conservatism or labour reform in the North, and so there were a wide range of opinions within the party. Someone like Horace Greeley (editor of the New York Daily Tribune, one of the largest GOP newspapers) openly supported labour reform both in America and in Europe. To a lot of abolitionists who would drift into the GOP (like Wendell Phillips) labour reform and antislavery went hand in hand. I imagine there would have been more than a few antislavery Democrats who also became Republicans after the Democratic Party became increasingly identified with slavery who had once identified with the Democratic Party as a pro-worker party. On the other hand, the party also had a strong conservative wing that in no way identified with the rights of workers. However, to extrapolate that to say they were pro-business is itself difficult: Pennsylvania manufacturing businesses wanted a tariff, while New York merchants were vehemently free trade. Other 'pro-business' issues like subsidies for internal improvements, the Pacific Railroad, and granting corporate charters often crossed party lines, especially at the state and local level. So it would be difficult to say the Republican Party started as a specifically pro-business party.

If you want to look at how Republicans grappled with whether it was a workers' or businessmen's party, though, look at the fierce battles for control over the party between Radicals and conservatives during Reconstruction and the Gilded Age. It's here that the party had to decide whether 'free labor' meant the right to sell one's labour in a competitive marketplace without restriction (or protection) or meant an activist state that gave protection to workers so that they might enjoy a standard of living. To many Republicans, it came to mean the former more than the latter - many leading Republicans noted during Reconstruction that the claims African-Americans made to slaveowners's real property (in the form of demands for redistribution of land so that they could survive without dependency on their former owners as vicious landlords) were similar to the demands that Northern workers made on their property in the form of taxation to fund unemployment and poor relief, regulation of their businesses, and what they perceived as theft through inflation, which labour groups often began to support. In short, the Republican Party became a bourgeois capitalist party for the same reason it turned against Reconstruction - the transformation of the post-Civil War economy pushed many leading Republicans to emphasise 'free labour' as market capitalism. If you want to read more, I'd suggest chapters of Reconstruction by Eric Foner (more Foner is always a good thing), The Monied Metropolis by Sven Beckert, and The Death of Reconstruction by Heather Cox Richardson, though Foner by far the most readable.

TL;DR: The post-industrialisation labour v. capital conceptualisation of class conflict implicit in a 'party of business' wasn't as clear in the 1850s as it would become later, but it was the transformation of the Northern economy in the 1860s and 1870s that emphasised the classical liberal capitalist aspects of antebellum antislavery ideology.

And as always, there are plenty of historians who would disagree with the above.