The party's assembly election manifesto pledges to find £200m of annual savings within 100 days of taking power.
The proceeds would largely fund policies such as cutting hospital waiting times and providing free social care for the elderly, Plaid Cymru said.
Leader Leanne Wood said Plaid had the "ideas and drive to build our nation".
By Spring 2017 Plaid would aim to raise annual savings to £300m, with the NHS saving a further £300m in efficiencies, and a new tuition fee policy £250m.
Students from Wales currently only pay £3,810 towards their tuition fees wherever they study in the UK with the rest, up to £5,190 a year, paid for by the Welsh government.
Under Plaid's plans, Welsh students working in Wales after graduation would receive £6,000 a year after graduating, up to a maximum of £18,000.
A cap on redundancy payments in the public sector would also save £40m, the party said.
Details: What is in Plaid's manifesto?
The party said NHS efficiency savings would be ploughed back into the health budget.  It also said the overall annual health budget would be £925m higher by 2020-21 than in 2015-16.
Plaid Cymru's plans for government include integrating much of health and social care, with local councils put in charge of community services, such as GPs' surgeries, district nurses and mental health.
An extra 1,000 doctors and 5,000 nurses would be recruited, to help drive down waiting times.
In schools, there would also be a 10% pay boost for teachers who gain extra skills.
Severn crossing tolls would be abolished for people living in Wales, if the powers are devolved from Westminster, the party said.
"We recognise Wales as a political nation in its own right," Ms Wood said.
"Which is why our country should have the tools to act like a nation, to innovate, to create jobs and to deliver world class-class public services."
She said there was a chance to build a "new kind of society" in Wales that "promotes equality, creates wealth, shares wealth and broadens life chances".
The manifesto states an independent Wales "remains our long-term aspiration as a party" but there are no plans to hold a referendum on the issue "in the near term".
Plaid said its government programme had been independently checked, for the first time, by academics at Cardiff Metropolitan University.
Prof Brian Morgan and Prof Gerry Holtham said the "overall income projections and the estimated costings" seemed to be "reasonable".
But they warned the "greatest uncertainty" concerned the efficiency savings.
"It is certainly the case raising these sums from efficiency gains is not going to be easy or painless," they said.
Plaid's 194-page document was the first party manifesto to be published during this assembly election campaign.
Plaid Cymru is trying to bring an element of freshness to the Welsh Government, partly by getting rid of old programmes and also by making efficiency savings to fund new ones.
So by spring 2017 the party says it will have found £1bn in savings to spend on its priorities - £300m will come from asking the NHS to work more efficiently.
But in a period when the Welsh Government budget has been feeling the pinch, it won't be easy.
Many of the policies have been announced before, including changing the tuition fee system so students will build up debt in future but can claim back up to £18,000 if they work in Wales after graduation.
After 17 years of Labour government Plaid says it is the change Wales needs.
To achieve that goal it will have to transform the electoral landscape, after a difficult few years since Leanne Wood took over as leader.
Plaid Cymru has said it will "re-direct" £1bn of the Welsh Government's £15bn budget, through ending some schemes and finding savings elsewhere.