The connection speed of the viewer and the pixels dimensions don't affect one another. I can post 2 800x600 jpgs, and one will be 500k, and the other 60k. It's all in the compression. If you have photoshop, use save for web and put the quality between 40-60 and you'll get a nice file size vs qualtiy. You can view the original next to your compressed version and check for quality. As for pixel dimensions, that will be affected by the viewers screen resolution. It was generally accepted that the average user had a resolution of 800x600, but in recent years, with big monitors getting cheaper, I think 1024x768 is more standard.
Still, I try and keep mine under 800x600 for the most part, unless I want you guys to see more of the detail, but I always try and keep it under 1000 pixels wide.