Best way to clean this circuit board?

When I was in the electronics manufacturing business, we used dishsoap and water.

A board that age probably has a solvent-soluable coating on it, so if you want to clean down to the base metal and board material, you can wash it with lacquer thinner. Then, to keep it from corroding, you would have to recoat it with lacquer or a modern board coating, making sure you don't coat the conducting surfaces. Some board coatings are water based.

We used typewriter erasers, fiberglass rods and/or nylon bristle brushes to remove minor corrosion from pins, but too much rubbing will remove plating and contribute to more corrosion.

Be extremely careful if you try to resolder the pins. Too much heat will lift the pads and loosen the pins in the board. Unless you are an expert and had the right tools, that kind of damage would be impossible to repair.