And don't throw out your original scan after the conversion. Resaving JPEG files removes even more data. Postprocessing Scanning can introduce some annoying artifacts. An image editor's Despeckle filter should remove them in one or two passes. Your scanning software may include descreen functions.
Some scanners produce images with distinct color casts.
You can usually remove the cast using a simple Curves adjustment in an image-editing program. Save sharpening for after you resize the image and convert it from RGB to gray-scale. Be sure to use an Unsharp Mask filter rather than a raw Sharpen filter. It's easy to get crooked scans from flatbed scanners. Fortunately, Photoshop's Measure tool provides a simple way to straighten an image.