Earlier this month Joyce DiDonato opened Wigmore Hall's 2014/15 season with a programme that combined familiar, and very much less familiar, Italian and American music. "Don'tworry if you've never heard of Francesco Santoliquido" she told me a few days before the performance, "few people have. In the 30s he was a fascist in Italy, but in the early part of the 20th century he wrote this wonderfully rich and romantic music that reminds you of Puccini." When she introduced the songs on stage DiDonato drew attention to these "glimpses" of Cio-Cio San and Mimi before earning a laugh with her private name for Santoliquido: "Frankie Holywater". Then she brought the house down with her performance.

DiDonato is both "just Joyce from Kansas", the unstuffy natural communicator whose habitual recital encore is "Over the Rainbow", and a proselyting archaeologist of the more obscure byways of music history. These personas share equal billing in the makeup of the most critically acclaimed and popular mezzo soprano of our day. As the Telegraph reviewer said of her performance in Maria Stuarda earlier this year at the Royal Opera House, "bel canto of this quality has not been heard at Covent Garden for more than a generation … On the strength of this night alone, her name should rank in the operatic pantheon alongside the greatest legends of the past".

Next week DiDonato opens the Barbican's new classical season with the first in a series of five Artist Spotlight concerts that provide a summation of her career. There is a bel canto evening, baroque in the form of Handel's Alcina, the European premiere of a contemporary work written for her by American composer Jake Heggie, one of her masterclasses that have become minor YouTube sensations and a full-scale concert with the New York Philharmonic. A thread that runs through the season, and her career, is DiDonato's search for freshness, whether in singing new music, unearthing previously overlooked work or imposing herself on famous roles.

"The elephant in the room for opera singers, and classical musicians, is that we are competing against ghosts," she says. "Some of the audience might as well be listening to you through the earphones of their favourite recording. If you don't hold a note in the same way, or don't make an inflection in the same way, they notice. A performance can become as much about what you don't do, as what you actually present." And she admits to approaching some of the iconic roles with the thought that unimprovable performances have already been given: "Maria Stuarda is Dame Janet Baker for me; Cherubino is Frederica von Stade. So the only hope you have for giving the audience a meaningful experience is to flush away any sense of competition and make the role belong to you, at least in that moment, because in 10 years' time it will surely belong to someone else. And if you can make it sound as if the work is being invented there and then you share something that is unique. But it does take a big investment. I feel as if I've been run over by a truck the morning after a performance of Maria Stuarda."

This sense of "making it new" is most apparent with contemporary music. "There is an obvious thrill in presenting something that people are coming to for the first time. They listen differently." But she says that "sensing the creative rush that gave birth to a new piece" is essential to looking afresh at established scores. "You want that same level of listening for The Barber of Seville, for music that might have been forgotten or in something like the baroque, where there is often very little guidance on the printed page. Coming from Kansas City I have a sensibility to jazz, and there are similarities – you have to infuse the music with variation and colour and you are given huge licence to leave your artistic fingerprint. Of course there is a certain amount of risk involved, but it is worth it."

Joyce Flaherty – the DiDonato came from her first husband – was born in 1969 and brought up the sixth of seven children in a Kansas City suburb. She says that as a child she could not have conceived of the career she has had. "I was overweight, had no self-confidence, one boyfriend – who turned out to be gay – and I only really fitted in with the choir. Even there I was never the star, although I would be put in the second sopranos because I could lead the section with the intricate harmonies. But as for being a professional? Never. I just wasn't that girl."

Instead she trained as a high school music teacher, but while at college took her singing increasingly seriously. By her final year she was "considering this opera thing" when she saw Cecilia Bartoli, who was about to blaze a trail in similar repertoire, in a PBS television special. "I'd never heard anything like it. We are only a few years apart, but in terms of career she is almost a generation ahead of me. She was singing Rossini's "Una voce poco fa" from The Barber of Seville, a piece I was working on at the time, and it was as if I had never heard it before. All of a sudden the bar was raised. Without any apology, she was showing raw joy on the stage. Marilyn Horne and Teresa Berganza and other iconic figures were of the era where it was about 'being an opera singer'. Bartoli ripped all that up. The biggest thing I've taken from her is permission to show I am actually enjoying it."

DiDonato was taken on to the Santa Fe Opera apprentice scheme and then, in 1996, the Houston Grand Opera young artist programme. But instead of her career taking off, it stalled as she was advised to completely remodel her vocal technique, a process that took three years. "It was very frustrating seeing all these people whizzing by me. When I left Houston I was the only one out of eight singers who couldn't get management." On a 16-day audition tour only one opera house out of 13 – well done, Paris – offered her a job. "Everything has always come late, such as a record contract; I was 35 making my Met debut when 29 is considered old. I always was a stage animal and a good and diligent musician. It's just that the voice was the last piece of the puzzle to kick in."

And when she did break through things weren't always easy. Long before the row over sexist comments about a female singer's costume at Glyndebourne this year DiDonato endured "one of the most humiliating experiences of my life in a costume fitting. I was a bit heavier than I am now and the male designer just turned to someone else in the room and said 'What am I supposed to do with her?' Of course I was angry. But my character had a lot of anger and so I tried to use it and actually got a lot of attention for my portrayal."

By the time DiDonato was established in her career a lot had changed in her life. She and Alex DiDonato had met as freshmen and married at 21. "That's what you did in the midwest. He's a great guy, but I didn't have a clue as to who I was or what I was doing. We were together for 14 years and then the world opened up and I didn't fit so well with the midwest model I had been living." DiDonato has been married and divorced again – to conductor Leonardo Vordoni – and says her late 20s and early 30s were a struggle to reconcile her background with her new career. "My family are my biggest cheerleaders now, but there were growing pains for them as well. My brother once said, 'Please don't change'. I said, "No offence, but I hope that I do change. I don't think my essence ever did, but I wanted to give myself the option to grow, learn, discover, succeed and fail. And to shed my midwestern Catholic guilt. It's still a work in progress but I am much further along that path."

She says there was no career plan: "It was job by job. Hang on to whatever coattails go by." But soon she was headlining in all the great opera houses, had a packed recital schedule, award-winning recordings – 2010 Gramophone artist of the year, 2012 Grammy for best classical vocal solo – and a growing public profile through performances at the Last Night of the Proms, not to mention the time she broke her leg onstage at Covent Garden in 2009, yet completed the performance and sang the remainder of the run from a wheelchair, sporting a pink plaster cast.

"And these days I can express opinions about costumes," she laughs. "And many other things." She has used her raised profile to promote issues of equality – most prominently around LGBT – and to campaign for arts education. "It still upsets me the way men are held to very different standards to women. I'm very curious how that will play out as we go into the US presidential election. My big ambition is to sing at the inauguration of President Hillary Clinton in January 2016."

In terms of repertoire she says the comparatively slow start to her career has provided her with a "sense of confidence that I probably wouldn't have had if things had come easier or quicker. I know I have put in the work, which now allows me to take opportunities as they come, as well as earning the right to a few risks."

An example is her new recording of mid-19th-century bel canto arias, Stella di Napoli, that forms the basis of her first Barbican concert. "There was a period of 20 years or so when there was a volcanic eruption of music. Not all of it is great, but the conductor Riccardo Minasi spent a long time with dusty and sometimes illegible manuscripts in the library in Naples, and we have uncovered some real jewels."

The project follows on from a previous recording, Drama Queens, which did a similar thing with baroque music, and DiDonato says there is much more material to be mined. "There is also a bridge between those two worlds. How we get from Handel to Rossini is something that interests me a lot at the moment, and I pinch myself that I am in a position to pursue that interest. It wasn't until my late 30s that I finally told myself that this opera thing was working and was sustainable, so there will always be a little bit of 'I'm just Joyce from Kansas, don't tell anyone this is happening'. But somewhere I was given permission, and gave permission to myself, to be 'that girl'. Having come this far I would be so angry with myself if I didn't enjoy it. So I do."

• Stella di Napoli is available on Warner Classics. Joyce DiDonato Artist Spotlight is at the Barbican, London EC2Y, from 25 September. barbican.org.uk.