U.S. businesses witnessed two very different sides of Donald Trump during the presidential campaign—the populist who railed against elites, global trade and unchecked immigration, and the more traditional Republican who promised to temper the regulatory state and overhaul the tax code.

Whatever view, or combination of views, that emerges from the White House will chart the course of American corporations for the next four years.

The stock market has clearly made its initial call, including a 2.9% climb in the Dow Jones Industrial Average since the Nov. 8 election with investor bets on new infrastructure spending and passage of corporate tax breaks.

Yet within nearly every sector, including energy, finance, media and technology, the competing ideas embodied in the president-elect’s past statements and roster of advisers need to be resolved before the economic picture clears.

Construction companies are enthralled by the prospect of a push on infrastructure spending, but are nervous over tariffs on imported goods or curbs on immigration. Big banks are heartened by the prospects of a regulatory retreat, but are concerned about attacks over their size. Media and telecom giants want Republicans to pump the brakes on rules governing internet traffic, but are wary of a more aggressive antitrust assault.

One possibility is a fusion of the populist and establishment agendas that yields a bigger federal role in infrastructure or antitrust policy, for instance, along with a lighter government touch on energy and banking.

For now, the jury is still out for many businesses, said Rob O’Neill, chief executive of American Hotel Income Properties REIT, which owns hotels that serve the freight industry.

“We like that the coal miners are going to be put back to work…That will mean our rail hotels and those regions filling up,” he told analysts last week.

Mr. O’Neill said he also worried an immigration crackdown would make it harder to hire workers: “What we don’t like are the issues surrounding the Hispanic population, many of whom make up our best and most loyal associates in the hotel operators teams.”

The GOP establishment, which watched as Mr. Trump attacked trade deals it once championed, is now hopeful the president-elect will collaborate with a Republican Congress to bridge their differences.
Given Mr. Trump’s push for more growth and jobs, “there is a giant nexus of crossover with Trump and all of his advisers,” said Bruce Josten, head of government affairs at the U.S. Chamber of Commerce, which had chilly relations with the Trump campaign for months.

On trade, Mr. Josten said, there may still be “some bumps in the road.” Yet the pick of Republican National Committee Chairman Reince Priebus as chief of staff, he added, is an early sign that “Trump and his inner-circle realize they need Congress to do a lot of the things he wants to get done.”

Industrial stocks have strongly outperformed the S&P 500 index since the election, as investors bet on a Trump infrastructure boom. That rally is predicated on an assumption some of the policies on which Mr. Trump campaigned won’t come to pass, especially the imposition of new tariffs and a retreat from free-trade agreements.

Mr. Trump’s push for more infrastructure spending and the possibility for a stronger dollar is “obviously good news for us,” said Bernd Scheifele, chief executive of German building materials concern HeidelbergCement AG.

“Trump is a doer. He’s an executor. He’s a deal maker,” he told analysts last week. “The down side is obviously…what happens to international trade agreements? What happens to Nafta?”

A Trump administration that unleashes oil and gas production and pursues a $1 trillion infrastructure package would prove a boon to such makers of industrial equipment as General Electric Co., Honeywell International Inc. and Rockwell Automation Inc.

On the other hand, Mr. Trump could ding the sector if he follows through on pledges to penalize businesses that move factories to Mexico and other lower-cost countries.

Mexico is a sore point among some major manufacturers after Mr. Trump criticized the closure of a Carrier Corp. air-conditioning plant this year. United Technologies, Carrier’s corporate parent said in February that it would close a pair of factories in Indiana, including Carrier’s Indianapolis facility, shifting more than 2,000 jobs to Monterrey, Mexico.

“Our largest manufacturing facility by employment is in Mexico, and our Mexican facilities are an important part of our supply chain. If the border were closed, it would be a significant disruption,” Ted Crandall, chief financial officer at Milwaukee, Wis.-based Rockwell, told shareholders last week.

In energy, Mr. Trump promised during the campaign to cancel the Paris climate accord and cut regulations that have held back oil and gas drilling. During his campaign, Mr. Trump pledged to end the so-called war on coal.

“He’s right. The war is over,” said Ian Robertson, chief executive of Algonquin Power & Utilities Corp, on an earnings call last week. “The bad news, at least for coal, is that coal lost” to market forces, not politics.

Electric utilities that buy more than 95% of the coal mined in America have retired hundreds of coal-burning plants and embraced natural gas, which is now a cheaper fossil fuel. Natural gas has turned abundant since innovations in hydraulic fracturing and horizontal drilling. Many say they are unlikely to reverse course now, even if regulations ease.

On Wall Street, many firms stand to benefit if Mr. Trump takes a deregulatory tack. His appointees could halt or reverse regulations on the “fiduciary duty” of investment advisers, risk-management standards for large insurers and asset managers, and consumer-finance rules governing everything from mortgages to bank overdraft fees.

GOP control of Congress also will ease the way to achieve such industry goals as curbs on the Consumer Financial Protection Bureau.

On the other hand, parts of the industry have much invested in the new rules. Tearing them up could require other unpopular trade-offs, such as higher capital standards.

Beyond the uncertainties in various sectors is the bigger one of who Mr. Trump picks to lead his agencies. Businesses are watching closely and seeking to exert influence as his transition team floats various names. The choices the new administration makes will help define its priorities and intentions.

“Appointments represent an attitude and direction towards policy,” said John Engler, president of the Business Roundtable, which represents large U.S. corporations.