The modern primary system only dates back to the 1970's and 1980's, that is long after Alaska and Hawaii joined the Union. As for future states, while territories like Guam and Puerto Rico do send delegate to the electoral college so have no role in electing the President of the United States, they are also on the contemporary primary calendar so are involved with choosing candidates. Puerto Rico has held a nominating contest (primary or caucus) since at least 1980, though I can't find a record of an earlier nominating contest. Regardless, if a territory were to become a state, it would already have a place on the schedule.

But before ~1972, there were some primaries and caucuses but often the results didn't matter that much for the final nomination, which was decided at the convention itself. This was often described as a process of party elites horse trading a smoke filled room. Delegates to these conventions were selected in a variety of ways, but most of them were not selected directly by voters. The first primaries came about in the Progressive Era, but they were often not binding. New Hampshire traditionally held the earliest primary, and that was a tradition that was maintained in the modern primary system. I heard on the 538 podcast this week that Iowa got to be first because McGovern (who helped write the rules) realized that a caucus could be held before the first primary in New Hampshire. As for Iowa specifically, 538 writers

While the state has been holding caucuses since 1846, it’s only had its first-in-the-nation status since 1972. And not until 1980 did the caucuses truly claim their reputation as the Olympics of pandering, the place where an underdog candidate could become a made man.

This was apparently mainly because Jimmy Carter was able to use a win in Iowa (technically second to "uncommitted") in 1976 to catapult himself into front runner status, which was confirmed by a win in New Hampshire shortly after showing that he could even win over Northern Liberals. Since the modern system originates at its earliest in the 1972 Democratic nomination process, in the 1970's candidates were still just learning the ropes and arguably the full system wasn't in place. Indeed, as late 1976, not all states conducted primaries/caucuses and not all candidates seemed to realize that the early nominating contests in small, out of the way states would actually be important. Some books, like the Party Decides, therefore only really count the modern primary system from 1980. Still, the two democratic candidates picked in the 1970's (the radically left McGovern and Southern Carter) were candidates who would never have been picked in the old, back-room dealings that formerly chose the presidency and showed that a canny understanding of the rules of the new system (McGovern focusing on delegate counts, Carter focusing on winning the earliest nominating contests) could make these outsiders winners.

Now, New Hampshire held the role as first in the nation even before the emergence of the modern primary process, where voters (for the most part) decide delegates to the convention. It has been first in the nation since 1920, and this status is both enshrined in state law and recognized by the parties. Even under the old system, it proved important. In 1968, Gene McCarthy did remarkably well against LBJ while LBJ was an incumbent, showing the widespread discontentment among the Democratic base with Johnson's presidency, especially the Vietnam War. This ended up with LBJ withdrawing from the nominating contest (as far as I know, the only elected incumbent ever to do so), which set up the very chaotic nominating contest (the assassination of RFK only made it worse) and the even more chaotic 1968 convention in Chicago, where Humphrey was chosen as the candidate despite never winning a single nominating election. This led to the reform of the rules, and the modern party system.

In the modern system, states often jockey to see who can get a better (usually, but not necessarily earlier) position. Conventions have always happened the summer before the election, so primary voting must be wrapped up by then, but this jockeying has lead to an earlier and earlier start time for the primary season. Here's wikipedia

Since 1977, New Hampshire has fought hard to keep its timing as the first primary (while Iowa has the first caucus a few days sooner) [...]. As a result, the state has moved its primary earlier in the year to remain the first. The [New Hampshire] primary was held on the following dates: 1952-1968, second Tuesday in March; 1972, first Tuesday in March; 1976–1984, fourth Tuesday in February; 1988–1996, third Tuesday in February; 2000, first Tuesday in February (February 1); 2004, fourth Tuesday in January (January 27). The shifts have been to compete with changing primary dates in other states. The primary dates for 2008 (January 8) and 2012 (January 10) continued the trend - they were held the second Tuesday in January both years.

This year this has been brought under control, and we're having the latest start since 1996. States have traditionally been generally free to chose their own primary dates (parties choose the date for caucuses), but Iowa and New Hampshire have worked hard to preserve their "first in the nation" statuses. The Nevada caucuses and the South Carolina primary are enshrined as the other two early states, but this very recent. Nevada only gained that position in 2008, apparently at the instigation of Harry Reid, who argued that his (heavily Hispanic and suburban) home state would make a great counterweight to the more rural and white voting of Iowa and New Hampshire. South Carolina's early importance is also recent also only dates back to 2008--it's important to Republicans as the "first in the South" elections and important to Democrats as the first state with a large African-American population. South Carolina had been pushing earlier (participating in the "mini-Tuesday" where five states chose to conduct earlier than usual elections in 2004) but in, say, the 80's and 90's wasn't a particularly early state.

So New Hampshire has a long legacy of being first in the nation primary even before it mattered to be first, Iowa ended up first Caucus through a clever gaming of the rules by McGovern in 1972 and both maintained their positions by stubbornness and boosterism. As other states tried to establish similarly important positions, the parties chose Nevada (in the West and heavily Hispanic) and South Carolina (in the South and heavily white) to add balance to the Iowa and New Hampshire.

Other states tried to similarly move up--Louisiana held the first primary that no one much paid attention to in 1992, for a few years Maine tried to establish itself as the second caucus--but these days the parties and the states have agreed to have these be the official "first four". In 2006, the Democratic National Committee decided that only the four states of Iowa, New Hampshire, Nevada, and South Carolina could hold primaries or caucuses before February 5, 2008. When Florida and Michigan tried to "jump the line", they were punished, none of the candidates campaigned there and the DNC only ended up seating half their candidates. Super Tuesday used to be a day when many large, important states happened to hold primaries (in 1984, there were three different "Super Tuesdays"), often the first or second Tuesday in March, but has become the day when it's now "open season" for any state to hold a primary. By 2008, this was about half the total number of delegates up for grabs on a single day. This cycle, things have become more spread out and many of the traditional Super Tuesday states (like California) are not participating so early (new rules and the length of recent nominating contests seem to have had the desired effect of encouraging states to spread out slightly) and some have taken to calling this the "SEC Primary", after the mostly Southern college athletic conference, rather than Super Tuesday.

For more on how the modern system developed, see my question The US is just starting presidential primary season. The modern primary and caucus system only dates back to the 1970's. Why did both parties switch at the same to the new system? How did this change happen?.