I use Photoshop's Save For Web. This automatically creates a very efficient web image.
I use crop a lot, and for color balance I use Levels, usually auto does a great job. Under the Sharpen Image menu I use Unsharp Mask with preview turned on, then twiddle the 2 values until it looks best. Too much gets ugly.
Photoshop is expensive and not worth the price if these basic things are all you are doing. Since I have it and know it very well, it's what I use.
On the Mac you can use Preview to do all the basics for free. It gives good results. I'm sure PC has something similar you can use for free.
I never look at the file size. Like Ellis noted, you can have a large, quality image smaller than 100k. Very rare for a web image sized to fit in a browser to get larger than that.