REVERE – The School Committee and the city purchasing agent have picked a Lynn firm with experience building schools to start work on a new Paul Revere School as early as November.DeIulis Brothers Construction Company, Inc. submitted a winning bid of $12.74 million to build the school.”They have built several local schools in the area and have a very good reputation,” city construction consultant David Billings told committee members.The tentative building schedule calls for the school’s completion in March 2010. The total cost for construction, furnishings and other costs is $18.5 million.DeIulis built elementary schools in Woburn and Salem and a high school in Medford, as well as an addition to the Ford School in Lynn. Its current projects include renovating and expanding a circa-1850 school in Lynn into new quarters for Girls Incorporated.Building a new Paul Revere triggered a large-scale version of musical chairs with 400 Paul Revere students starting school at the Beachmont School in August. Over 400 middle school students who attended Beachmont for the last several years moved in August into the new Rumney Marsh Academy.The city’s newest middle school is located on American Legion Highway. It cost about $27 million to build and its 50 rooms include 34 classrooms, a 200-seat auditorium, basketball court and a cafeteria with plenty of natural light.Although the city received 90 percent state reimbursement approval for Rumney’s cost, the city must borrow money and dig into the taxpayers’ pockets to pay for Paul Revere.Unlike the three public schools Revere has built since 2006 – Whelan Elementary, Anthony Middle and Rumney – Revere will be paid for with a combination of a state loan to the city and state money, plus the city’s contribution.Mayor Thomas Ambrosino thinks the timing for building a new school is good: Many other communities are a year away from completing design work necessary to start school projects and construction firms are competing for jobs in a slowing economy.