Whichever route you choose depends on how you want your graphic to look, it is your choice. Both Adobe Photoshop and Adobe ImageReady have built-in tools which help optimize images for viewing over the web. The best bet is to use whichever software you are most comfortable with. If you are already familiar with Photoshop then using ImageReady is unnecessary.
The easy way:
The Photoshop "Save As" control lets you save an image as either a GIF, JPEG, or PNG file. You can designate image quality, background transparency or matting, color display, and downloading method depending on which file format you select.
The controls for each of the resulting dialog boxes are pretty much self explanatory. I recommend saving your image this way (using a different name) and then saving it using the next steps as a way of comparing the two. Doing it this way will give you a good indication of which option gives the best results.