Mayor Thomas Menino submitted his final city budget this week, proposing an increase in spending to $2.6 billion. The fiscal year 2014 proposal, which is Menino’s twentieth budget and which must be approved by the City Council, includes funds for the first “digital school,” the first smart parking sensors, and the first bike helmet vending machines and tests out new “girls only” times at community centers.

Menino, who announced last month that he will not be seeking a sixth term, has also set aside $50,000 for the new mayor to transition into the job Menino has held for five terms.

The budget increase is $139 million, or 5.6 percent – the largest since fiscal year 2008, when it came to a 6.2 percent increase. The increase in last year’s budget was $72 million, or 3 percent, to $2.4 billion.

“We have worked to open up this city and the opportunities in it to people from all backgrounds and places,” Menino wrote in an April 8 letter to the City Council. “The annual budget process is essentially one of exercising the public trust. We have strived to meet that trust by being prudent and by being inventive, and most of all by being fair. The FY14 budget includes resources to help this administration share any lessons that might be sought by the next one. I am confident, however, that the pursuit of opportunity for all of our people would transfer in any event because it is at the root of who we are.”

The proposal will become the focus of City Council hearings for the next three months, as several city councillors jockey to succeed Menino.

The budget adds a number of full-time employees to the city’s payroll, including the addition of a person in the city’s arts and tourism department to handle booking for the Strand Theatre in Uphams Corner. Three people on the department’s staff also handle the Strand, which is receiving an influx of $1.2 million for upgrades and improvements, the last phase in an improvement project.

The Inspectional Services Department (ISD) is also adding 12 new positions, which are necessary due to a new rental housing ordinance, administration officials said. The ordinance, approved by the City Council last year, requires the annual registration of all rental units and establishes a public “chronic offender” registry. And the Boston Centers for Youth and Families is also hiring two street workers.

The city’s school department has a proposed budget of $934.6 million for fiscal 2014, an increase of $60.8 million from fiscal 2013. The increase comes as 1,200 new students are expected to enter the system this fall, bringing the overall number to 58,200, the highest since 2005.

“This budget represents another important step forward for the Boston Public Schools,” School Committee Chair Michael O’Neill said in a statement after the seven-member committee unanimously passed the budget in March. “It continues our focus on quality and puts as many resources directly into our schools as possible. It supports our vision for more inclusive learning opportunities, more dual-language programs, and an expansion of K-8 schools.”