Mayor London Breed’s proposed budget for the coming fiscal year will soar by $1.2 billion — making it the largest in city history — and boost investment in tackling the city’s most urgent problems: housing and homelessness.

The mayor’s $12.3 billion budget would be a 10.8% increase from last fiscal year, which came in at $11.1 billion. Much of the extra money, city officials said, came from $142.3 million in excess cash in a county education fund and “better than expected” property-transfer and business taxes.

But that doesn’t mean the city has $12.3 billion to freely spend — about half must go to so-called enterprise departments, such as the airport, Public Utilities Commission and Municipal Transportation Agency. Another portion must meet other specific needs, such as public libraries and parks, due to voter-approved mandates. And the city will be paying more salaries. The budget covers 31,830 full-time equivalent positions, up 0.8% from the previous year.

That leaves the mayor and the Board of Supervisors with $3.3 billion in the general fund to decide how to spend.

Breed announced her budget proposal Friday at the Sunnydale public housing project near Visitacion Valley after touring some of the dilapidated public housing units that are due to be replaced. In addition to replacing the units, the city plans to add nearly 1,000 affordable and market-rate homes to the site.

After visiting two apartments on Santos Street, where she chatted with residents, Breed proceeded to a nearby basketball court where nearly 400 people gathered to hear her budget priorities. She said the spending plan focuses on equity and accountability for all, including people in often overlooked communities like Sunnydale.

“Let us remember, our job is to be accountable to everyone in this city and not just the people who can show up and advocate at City Hall,” she said.

Board of Supervisors President Norman Yee, who joined Breed on her Friday tour, said he expected to quibble over details but agreed with the mayor’s spending priorities.

“I feel we’re in sync on what we see as the broad needs,” he said, citing homelessness, affordable housing and income inequality. “My role as a member of the board is to ask questions.”

Breed’s proposal next heads to the board’s two-month review, led by Budget Committee Chairwoman Sandra Lee Fewer. The board is expected to propose changes during that process. The budget must be completed and signed by the mayor no later than Aug. 1.

The mayor’s proposal includes funding for two years, fiscal years 2019-20 and 2020-21. The second year’s projected budget is expected to drop slightly to $11.9 billion because: some one-time capital project expenditures will end; and the amount of excess cash from the county education fund will shrink. The Educational Revenue Augmentation Fund, a state program, shifts a portion of local property taxes to public school systems in each county. When officials determine it has enough money to meet the minimum state funding for public schools and community colleges, the excess funds are turned over to local governments.

But the rosy budget doesn’t reflect some challenges. In January, the mayor and controller said the city was facing a projected $270.8 million deficit over two years. In March, that was revised down to $156 million. Rising employee costs, voter-approved set-asides and state-mandated policy changes are expected to increase expenses in the coming years. Officials in the mayor’s office say they’ve got a handle on that, however, due to slightly better than expected revenues, efforts by departments to rein in spending and increases in state funding for in-home support services.

But Breed, for now, is focused on how to spend the extra funds in the upcoming budget. Here’s where she’d like some increased spending:

Homelessness: A major chunk of Breed’s proposal — over $100 million in additional funding — would increase and support homeless services over two years, helping Breed meet her campaign goal of 1,000 new shelter beds by 2020.

Affordable housing: Breed proposes over $118 million to buy land and build 100% affordable housing, and another $10.5 million to fund a five-year, rent subsidy program for 350 low-income households and seniors struggling to pay rent.

“It’s all about housing,” Breed said at the Sunnydale event. “We all know the cost of housing is too high. We all know the problem did not happen overnight and will not be solved overnight.”

Mental health services: Another $50 million would help expand the city’s behavioral health system, which includes more than 100 treatment and recovery beds for those suffering from mental illness and substance abuse.

“Combined with the 100 beds we already announced earlier this year, that means we are committing 200 new beds for our most vulnerable residents this year alone,” Breed said. “That is the most significant expansion of behavioral health beds in a generation.”

Equity programs: The mayor also plans to increase investments in equity programs that would benefit children and young people. That includes a $15 million annual commitment for Free City College and $10 million for teacher stipends to keep educators at schools that typically have high turnover.

Transportation, small business and street cleaning: Breed’s investments include $30 million for transit, such as purchasing new light-rail trains and upgrading the train control system, $9 million for city programs that help small businesses, and $11.9 million over two years to fund seven new public toilets, Bigbelly trash cans and street cleaning.

Trisha Thadani is a San Francisco Chronicle staff writer. Email: tthadani@sfchronicle.com Twitter: @TrishaThadani