well, you are going to have to cut quality to meet the size limits, but if you consider that very few people have screens larger than 1140x1050, you can cut size to about that, and if you have photoshop, setting Jpeg quality to 10 insted of 12 will reduce file size by about 70% with no drop in quality onscreen.
Avoiding compression is only really needed if you want to continue editing a pic, and any resolution higher than screen is only really needed if you want to either print or zoom in.
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