Like you, I save as psd. Everytime you make an alteration to a jpeg and then save, it will attempt to further compress as you state.
I find screen images usually improve with a little sharpening. It probably depends on the degree of manipulation already applied within the particular camera.
Printed images likewise benefit from sharpening in my case, but I think you will have to experiment with prints, as what you see on the screen can differ markedly from how a print turns out, regarding brightness, contrast and colour saturation.