Massachusetts House lawmakers began debate Wednesday on a proposed $57.9 billion state budget for the 2025 fiscal year that would include $500 million for the state’s emergency shelter system. Budget writers said the plan also includes a record $555 million investment for the Massachusetts Bay Transportation Authority. Democratic House Speaker Ronald Mariano has said spending on public transit is key to the state’s economy. Budget writers said they were able to create a spending plan without dipping into the state’s rainy day fund. Under the plan, the fund is on track to top $9 billion.