If I recall my GIMP correctly, you need to Scale the picture. There's two different subjects. Resizing is for print and Scaling is "resizing" the actual pixels on the screen...but I might be a bit muddled on that (sorry, I'm tired). Also, if you save as a JPG, its a balancing act to not have a huge file but keep the quality high enough you don't see degradation. You may have to save a couple of different times and compare the file sizes. GIMP may also have a tool that allows you to tweak the quality and see the kb changes. JPG's are saved as "lossy" files. Basically to condense them for the web, the JPG process strips the extras from the picture that don't have an immediate impact on the image. But you start getting poorer and poorer quality the smaller kb you go.
But you want to crop your image first! Get rid of the void space and you don't have to mess with it taking up memory when scaling. After that you can worry about scaling and JPG lossy files.
But it should be easier to get closer to the size you need.
I know I have to save, check kb size, tweak here, tweak there, etc. several times before I get the file to fit within the parameters but still be the best it can possibly be. It will just take time to get used to it. Oh and GIMP has a surprisingly good help/FAQ documentation. Don't hesitate to use it as it has a lot of good information.
Good luck!
OH PS - make sure you have the box checked to maintain the Ratio or Proportions of the picture. If you change one side, without the check box, it will skew your image, which sounds like it might be part of your troubles.