A new kindergarten center scheduled to open in September is expected to help alleviate overcrowding in Braintree’s elementary schools. But the project will also squeeze the school system’s budget, forcing administrators and officials to make tough funding choices as they begin drafting a budget. Department heads and principals from Braintree’s nine public schools met last week to pitch funding priorities to the School Committee, but Mayor Joseph Sullivan warned no school would get everything it requested. “They come to advocate for their specific school and for particular improvements to their curriculum,” Sullivan said. “That’s important, but I underlined the point that we are one system.” The planned Monatiquot school will partially occupy space formerly used by the Montessori school. Renovations to the building will cost about $175,000, Sullivan said, while running the school will cost about around $650,000 annually. Sullivan said the town hoped the state Legislature would pass a bill giving more unrestricted local aid to municipalities, but was not holding its breath. “We’re not waiting around for the Legislature,” Sullivan said. “We need to open Monatiquot, and we need to do it in professional yet prudent way.” Sullivan said Braintree was on solid financial footing, but needed to balance school funding with other priorities, like public safety. The town recently hired three new police officers and four firefighters.