Square drive screws are the best way to go. You can easily put them in very tight and also get them back out again. Phillips head screws tend to strip. A bit of history, Henry Ford apparently wanted to use the square drive screws for his Model T but did not want to pay the patent holder. Robertson would not give them away free to Ford. So Ford came up with the Phillips head - a plague on all builders.
As for stainless and strength, I have a 38 foot 54 year old 38 foot wooden sailboat. Over the years I have used many hundreds of stainless screws from small #6 to # 14. They get tightened very tight and do not break.
As for corrosion - most sailboats have many SS screws in aluminum masts and do not have problems.
For any screw application if a store does not have square socket screws I go elsewhere - whether SS or normal household mild metal.