On May 10 senator Rand Paul will travel to Iowa to attend a decidedly innocuous-sounding Lincoln Day dinner being held by the state's Republican party. Paul will give a speech and press the flesh with local party dignitaries in the city of Cedar Rapids, smack in the middle of the American heartland and far from the corridors of real power back in Washington DC.

It sounds like just another day of low-level humdrum politicking. But, of course, that could not be further from the truth. Iowa Republicans will be the first to cast their votes in the GOP's presidential nomination battle for 2016 and Paul – a Tea Party favourite and rising star of the conservative right – is almost certain to have his name on that ballot.

It has been a remarkable rise. Just four years ago, Paul was an eye doctor living in a small town in Kentucky and little heard of outside the libertarian-leaning circles that idolised his father, right-wing Texas congressman Ron Paul.

Now Paul, 50, is a senator and firmly established as the inheritor of his father's political movement. He is a leading light of the Republican party and hotly tipped to run for the White House himself. When he speaks in Cedar Rapids it won't be an obscure dinner function. It will be one more careful step on an ambitious road to power for a man rapidly becoming used to creating national headlines.

Paul has never been more in the spotlight. This week he gave a speech to the Hispanic Chamber of Commerce in which he came out in favour of immigration reform, putting him at the forefront of Republican efforts to woo a demographic seen as vital to any political movement seeking power in the US.

That came on the back of Paul winning the straw poll last weekend at the powerful conclave of conservative activists known as CPAC. Held at a fancy convention complex outside Washington DC, the gathering saw a veritable beauty parade of "new generation" conservatives vie for attention. But Paul came out on top, pipping Florida senator Marco Rubio by 25% to 23%.

'There is no way the GOP is going to get anywhere without Rand Paul' says one supporter. Photograph: Alex Wong/Getty Images

No doubt part of the reason behind that win was Paul's performance when he launched a recent remarkable 13-hour filibuster on the floor of the Senate against aspects of Barack Obama's controversial drones policy. The move, which began as a lonely stand in an empty chamber, eventually rallied support across the party's right, went viral on the internet and even won over a Democrat to join him.

For Michael Graham, an influential conservative radio talk show host, Paul's emergence has been an exciting breath of fresh air. "I am hopeful that he runs for president in 2016. He shows the value of having a clear ideology and advocating for it," Graham told the Guardian.

That ideology – a libertarian-soaked philosophy of small government, free markets and strict constitutionalism – has been to a large extent inherited from his father. Over successive failed presidential campaigns Ron Paul turned from laughable outsider to respected gadfly to the head of an enthusiastic grassroots conservative movement whose overwhelmingly young followers have a major impact on the Republican party.

When the congressman retired last year it was in front of an audience of thousands gathered in Tampa, Florida, determined to make their mark on the Republican national convention that followed shortly after. It also came after his supporters waged a campaign at the state party level that successfully took over several state party organisations.

Rand Paul has now largely inherited those fans, many of whom refer to themselves as the Liberty Movement. Evan Kenney, who was a delegate in Tampa, is a member of that movement and now running for local office in Massachusetts where he is a student.

He welcomed the passing of the torch from father to son, not least because the younger Paul's political skills appear more smooth and polished. "Ron Paul was a purist, but Rand Paul can do a much better job of doing the politics. He has a more moderate approach and feel, but it is the same end game," Kenney said.

That difference was on full display this week. Whereas Paul senior has been against immigration reform and is famously irascible in his speeches, the younger Paul peppered his talk in favour of reform with Spanish phrases, humble anecdotes about his Texan childhood and quotes from Pablo Neruda and Gabriel García Márquez.

But while Paul has embraced the idea of immigration reform, he was far more concerned about solving a political problem – how to win over Hispanics – than a policy one. His speech contained much sentiment, but few specifics. Nor did it mark a transformation of Paul away from the Republican right: just days before he had announced the introduction of legislation in the Senate aimed at effectively outlawing abortions by counting fetuses as citizens.

Rand Paul is his father's son: 'Ron Paul was a purist, but Rand Paul can do a much better job of doing the politics.' Photograph: Joe Skipper/Reuters

That Paul should grow up a libertarian-leaning conservative is no surprise given his father's politics – though he is not named after libertarian heroine Ayn Rand as many mistakenly believe. But as a child, growing up in the town of Lake Jackson,Texas, just outside Houston, Paul was present at his father's first ever political speech in 1974. As a teenager he would travel to Washington DC to work as an intern in Paul's congressional office and, in 2007 and 2008, he campaigned on his father's presidential run.

But now Paul is definitely stepping out of his father's shadow, driving the Liberty Movement and many of its beliefs into the Republican party. "The father was very provocative, the son is more politically astute," said Doug Wead, a consultant who has long been close to the political circles around the Paul family. Wead added that Rand Paul had already gone a long way down the path of making his father's followers into a core part of the GOP coalition.

"There is no way the GOP is going to get anywhere without Rand Paul. They can't win a general election without him either somewhere on the ticket or with him as an enthusiastic backer of the candidate," Wead said.

Yet for much of Paul's adult life that would have seemed a ridiculous statement. He initially followed his father's footsteps, not into politics, but into medicine. Paul went to Baylor University and then won admission to Duke University's prestigious Medical School in North Carolina. He graduated as an eye specialist in 1993, two years after meeting and then marrying Kelley Ashby. The couple, who now have three children, moved to Kelley's home state of Kentucky, and Paul joined an eye clinic in the small university town of Bowling Green.

Paul's work was a success, and he quickly moved his growing family out of a one-storey home and into a gated community about five miles from downtown. He joined a local Presbyterian church, where Kelley became a deacon and their children played instruments at church events. "He's a good man. He's very committed and devoted person, whatever he does," said pastor Michael Covington, though he noted that Paul had recently switched congregations and joined a local Methodist church.

Though Paul had little to do with Republicans in Bowling Green, he did start a local group called Kentucky Taxpayers United, which was a sort of "Tea Party before the Tea Party" that campaigned on reducing government spending. It folded in 2000 but saw Paul appear on local television, and his letters were published in newspapers.

Then, as he helped his father run for office in 2007 and 2008, the financial crisis hit the US and the real Tea Party was born. Paul became active in the explosive movement and still maintains close links with its adherents in the state. The Louisville Tea Party is holding a "Stand with Rand" gala next month at which Paul will speak. The group's president, Sarah Durand, heaped praise on Paul. "We are very proud of him. He is one of the few people in Congress who defend the constitution," she said. "When you meet he is very down to earth. When he talks to you he's very honest. He will be upfront. He does not give you lip-service like other politicians."

That sort of devotion – and the fiery energy of the Tea Party movement – saw Paul jump into politics as the 2010 mid-term elections loomed. First he entered the Republican primary as a rank outsider against the establishment figure of Trey Grayson, a protege of powerful Kentucky senator Mitch McConnell. "If there's ever a year for an outsider who has never held office before, this is the year," Paul told a crowd as he announced his bid. He was right. Backed by endorsements from the likes of Sarah Palin, Paul beat Grayson by 23 points. That pitted him against the Democrat Jack Conway in November as the Republican elite moaned that such Tea Party rebellions would cost them seats. But Paul beat Conway too.

Yet the ideological fervour and plain-speaking that has seen him become a hero to many has got him into trouble too. During the 2010 campaign Paul made remarks critical of the landmark Civil Rights Act, seeing parts of it that outlawed racism in private businesses as an example of government interference and thus anathema to some true libertarians. Briefly, in the face of the resulting media storm, Paul went into retreat, cancelling an appearance on Meet The Press.

Paul walks to a waiting vehicle as he leaves the Capitol late at night after his filibuster. Photograph: Charles Dharapak/AP

Similarly he was rebuked, even by fellow Republicans and social conservatives, last year when he joked about gay marriage at a meeting in Iowa. He said: "The president recently weighed in on marriage and you know he said his views were evolving on marriage. Call me cynical, but I wasn't sure his views on marriage could get any gayer."

But, despite such gaffes, Paul is largely a sure-footed politician. Those who know him both in politics and his personal life describe a dedicated, focused man whose eyes are set firmly on his career path – a road that is currently headed towards running for president in 2016.

The vehicle for that journey will remain the Republican right. As conservatives shift their stances on issues like immigration, or try to project a softer, more sympathetic image, his core beliefs will be largely unchanged. He remains the champion of the Tea Party, libertarians and constitutional conservatives, just as his father was before him. Indeed, far from declining after Ron Paul stepped aside, Rand Paul is now taking that same movement into the Republican mainstream.

"He shows his personality, which is dogged and determined. Often times a movement needs a firebrand. Sometimes you need someone from those extremes. He is exactly where he needs to be," said Covington.