First, pick the screen resolution that you will be using most. I assume you know how to determine that since you mentioned resolution info. 500x546 is a totally non-standard resolution and I have no idea where you got that from!
Anyway. Let's say you want to use 800x600.
Method 1:
Make a new document in Photoshop with those dimensions. Now cut and paste your original image into that spot and move it around and/or resize (Command+T) as needed to make it fit as best it can in those dimensions.
Method 2:
Take your original image and choose Image/Image Size and enter 800 x 600 into the dimensions area (you may need to turn off Constrain Proportions). This isn't the best solution because it will disfigure your image since it's a different aspect ratio.
Method 3:
Open your original image and use the Crop tool with a fixed dimensions setting (top entry fields in Photoshop 6 for width/height and resolution). You'll enter 800 pt, 600 pt and 72 respectively. Now drag the constrained Crop tool over your image to your liking, hit enter and you'll have the perfectly sized image.
There's probably 43 other ways to do this, but these are the first ones that came to mind.
I also think you can pick a larger resolution, say 1024x768 and the system will scale down accordingly for lower resolution screens, though I'm not totally sure about that. Sounds right though.