there are many things that affect file size.
First lets talk raw files which is what the camera captures at the sensor. THAT file is always the same, it is LxWxD: length in pixels, width in pixels, depth (number of colors per pixel). So if you have a 1024x768 monitor with 8 bits of color (256 colors) you end up with 1024x768x8=6,291,456 bits or 6.2Mb or .78MB big. A 1024x768x32 bits of color (429 Million colors) = 3.14MB of file size.
A 450x951x32 bits ends up being 1.7MB big. So if you shoot in "raw" mode this is what you should expect to see saved to your memory stick/hard drive.
The JPEG file type has several different levels of compression and which one you or your software choose directly affects the file size. One example of compressing is taking 10,000 sequential 1's in your file it can be compressed down to 1 1 and something that says "10,000 of those things" so a pure white or pure black background is more easily compressed down to a smaller size than a "diagonal gradient" where every pixel is different from its neighbor in every direction. On minimum compression the algorithm would "say" "that is a different color pixel so I will record both" where on maximum compression it would say "that is within 10 or 20 shades of the next so I will merge them as the same". The more you compress, the more you get "jaggies" from that merging of "similar" pixels.
DPI (dots per inch) really doesn't apply to your monitor screen and only truly applies to printers. It represents how many dots of ink the printer can put down and/or how many you want it to put down (if that is less than the maximum the printer can do). If you are printing a small object you need less DPI because the "lines of differentiation" are closer together than when you print a big object. Imagine, you take your favorite pen picture and make a 3"x5" print of it. In this situation the edges of the pen are physically only 3/4" apart (nearly life size). The "lines of differentiation" of color (the grain, the slope of the nib, etc) are very close to each other so a few dots fills that in nicely. Now take the same photo and blow it up to 3'x5'! The edges of the pen will be 4" apart (12 x the 3/4" from before) and the "lines of differentiation" will be several inches apart. If you don't have enough DPI then that will look really carpy so you will want 300dpi or better. ((inline foot note: the optimum DPI for printing on epson photo printers is 360DPI.))
Your monitor, on the other hand, doesn't care about DPI, it only cares about pixels. If your camera could take a picture 1024x768x32 and your monitor supported 1024x768x32 that picture would look perfect on that monitor. If you displayed the picture edge to edge on a bigger monitor, it will look progressively worse as the monitor gets bigger because the monitor has to try to figure out how to "interpolate" what should be between each of the pixels that it actually knows about. (If you want to see this in real time open you picture in any editor and then zoom to 200% or 300%, etc).
So when saving you picture for the web, how does DPI affect your picture? It doesn't. But, your software tries to simplify your life and not get into the DPI vs Pixel/Print vs Display discussion and simplifies it all down.
So in the terms of what you software will tell you about, to make your picture good for the web you want to "resize" your photo to 800x600x72dpi in RGB mode (the norm) and, if your software has it, "Web ready" which will decrease the bits of color to the minimum to accurately represent your picture. I use those setting and "jpeg quality 8" which in my software is 1/3 compression and all my photos come out right around 100KB and look great.
If you are using Adobe Photoshop (vs photoshop elements which I don't remember) you resize the file by going to Image:resize. And when you crop it you can specify a DPI setting. So, I would do it in this order: Crop it to the size/shape you want (leave DPI alone to keep best quality); resize it to the size you want; "save as..." jpeg, quality 8, progressive. That will 95% of the time get you to what you need to post here and leave your original picture at full size/color depth so if you want to make the 3'x5' print in the future you still can.
GK