If you want to change dpi to 72, I'd suggest doing this first, then resizing your image to your desired proportions (1024x768 for example). No real need to calculate anything - let PS do it all for you.
When resampling, bicubic is one method, and nearest neighbour is another. It's up to you the best method of sharpening that is implemented when resizing your images. I like nearest neighbour in some instances, and in others it's too strong and I just revert to bicubic sharper.
There is a clear difference in quality between say maximum or 10 and 6 or 7. But between 8 and 9 or 9 and 10, it's very hard to tell. For web size, 7 or 8 should suffice.