If you're interested in the question of how valuable the Panama Canal was, and to whom the benefits accrued, you might want to take a look at "What T. R. Took: The Economic Impact of the Panama Canal, 1903–1937," by Noel Maurer and Carlos Yu in the JEH. (Working paper version here: https://www.hbs.edu/faculty/Publication%20Files/06-041.pdf) (They also wrote a book on the topic later, titled The Big Ditch.)

The answer to your question depends very much on the era. In the early period, the gains to having the Panama Canal were quite large, but they mostly accrued to the US in the form of lower transport prices. The US could have had to pay a very large premium to build the canal, or to use it once it was built. But this was the era of big stick diplomacy, and the US made substantial use of its military and diplomatic power to ensure it did not have to.

There had long been talk of building a canal between the oceans, with two major candidates, Panama and Nicaragua. The big questions were going to be: who got to control the canal (both in terms of who went through, and also who made decisions about taxation and so on) and who paid for the right to construct or use it. This would determine the value of a canal both to governments and to investors.

The negotiations that eventually led to the existing canal began between Colombia and the US, since Panama was at the time a part of that country. The Colombian government had the obvious advantage that they controlled the territory, and thus, knowing the US was interested, could theoretically extract all the extra value as a payment for its use. The US had two aces in their hand to counteract this. One, there was always the Nicaraguan option, and the US could claim to pursue this alternative if the price went too high. And two, the US could just threaten to send in the marines, if not to outright conquer the area, then at least install a friendly government who would negotiate.

In January 1903, the Americans' first bluff appeared to work. The Colombian government put pressure on their envoy Tomás Herrán to get an agreement signed, and the US threatened to pull out and switch to Nicaragua if they didn't agree to generous terms. Herrán caved, and thus the one-sided Hay-Herrán treaty was signed, guaranteeing the US more or less full control over the canal zone, in exchange for $10 million and an annual payment of $250,000. The Colombian government was not impressed, and the senate refused to ratify the treaty.

The rejection of Hay-Herrán caused the US to switch to plan B: big sticks. The US, via the French engineer Philippe Bunau-Varilla, backed an insurgency in Panama led by Manuel Amador. Hay then made publically clear that the US would not allow Colombia to intervene in the event of a rebellion. Panama then declared independence, which was immediately followed by a contingent of US marines disembarking, to prevent the Colombian government from doing anything about it. The US then disavowed any interference, but recognised the new government, and immediately went about signing the Hay-Bunau-Varilla treaty (Bunau-Varilla having not very mysteriously been made foreign minister of the newly independent Panama as part of the shady deal). This was much more generous even than Hay-Herrán to the US, granting effectively full sovereignty over the whole zone, with no taxation rights for the Panamanian government. (When the Panamanians tried themselves to renounce the treaty, the US sent in even more marines, just in case there was any question who was really calling the shots.) The US government, meanwhile, bought up the canal company, so this was now a US federal government asset.

So, there's the first part: the US got complete control of the canal zone, for cheap. Any benefit to the Panamanians from the initial purchase was blunted by the relatively low price, and the ongoing benefit was foregone because the US controlled the area.

The construction of the canal itself could have had substantial benefits to the local economy, but it was conducted almost entirely with labour imported from the British West Indies, and while there were higher tiers of job available (the "gold roll" skilled labour), those went almost exclusively to Americans - a grand total of 16 Panamanians were hired at that wage. The canal company even ran company stores, to soak up whatever demand-led growth the construction might have created. The US did create infrastructure as part of the canal building project, including sanitary works, but also charged the Panamanian government for it. The most beneficial enduring effect was an anti-malarial campaign that did lower mortality.

Until the 1970s, that was how the situation remained, with the near-total US control over the canal preventing the Panamanian state from doing much of anything with one of the world's largest pieces of infrastructure bisecting their country. Following the return of control to Panama with the Torrijos-Carter treaty, the Panamanian state has been able to both improve the management of the canal, and also turn it into a substantial source of state revenue. But I know less about that part of the history.