Jeb Bush has launched a Republican presidential bid months in the making with a vow to get Washington “out of the business of causing problems” and to stay true to his beliefs.

“I will campaign as I would serve, going everywhere, speaking to everyone, keeping my word, facing the issues without flinching,” Bush said as he opened his campaign at a rally near his south Florida home at Miami Dade College.

The institution’s large and diverse student body was chosen to symbolise the nation he says he seeks to lead.

• Hilary Clinton launches new online shop
• Speeches help Clintons earn $30 million a year

The former Florida governor, whose wife is Mexican-born, was addressing the packed college arena in English and Spanish, an unusual twist for a political speech aimed at a national audience.

“In any language,” Bush said, “my message will be an optimistic one because I am certain that we can make the decades just ahead in America the greatest time ever to be alive in this world.”

“We will take Washington – the static capital of this dynamic country – out of the business of causing problems,” said Bush, adding, “I will take nothing and no one for granted. I will run with heart. I will run to win.”

Bush enters a 2016 Republican contest that will test both his vision of conservatism and his ability to distance himself from family.

Former Secretary of State Hillary Rodham Clinton holds a commanding lead in the Democratic race, setting up the possibility of another Bush-Clinton presidential race after her husband Bill Clinton defeated incumbent President George HW Bush in 1992.

Neither his father, former President George HW Bush, nor his brother, former President George W Bush, attended Monday’s announcement.

The family was represented instead by Jeb Bush’s mother and former first lady, Barbara Bush – who once said that the country didn’t need yet another Bush as president – and by his son George P Bush, recently elected Texas land commissioner.

Before the event, the Bush campaign came out with a new logo – Jeb! – that conspicuously leaves out the Bush surname.

Bush joins the race in progress in some ways in a commanding position, in part because of his family connections.

He has probably raised a record amount of money to support his candidacy, allowing him to make a deep run into the Republican primaries. But on other measures, early public opinion polls among them, he has yet to break out.