Vehicle manufacturers use rubber bushes, not just on price, but they are an integral part of the ride quality. So don't discount original replacements. Many bushes are shaped to give more flex in some directions.
Plastic bushes, as this is what they are, will last longer a they are less susceptible to age deterioration. They will generally give a firmer ride, so handling may improve, but at the expense of noise and comfort.
Rubber bushes usually flex, but poly ones often do not, instead the moving component will turn in the bush. Many will squeak as a result.
My advice would be to get the softest you an find, as they will be closest to the flexibility of the original rubber, unless you intend to do any motorsport, where stiffer ones may suit better.
If replacement rubber ones are available, that may be the best solution.