http://www.gimp.org/downloads/
download gimp, you can convert, resize and convert to other formats.
Its a free public license program.
A photoshop if you will with a few features missing, but it doesnt cost $250 either.. :D
There are also a number of only tools that you can use such as
http://www.getpaint.net
You will undoubtedly want to resample and reduce the size of the pic as well as reducing the color to 16bit in order to reach your 1kb limit. that is not a lot of space at all..
Start by converting to a 16bit .gif image, btw.
Good Luck,
Have Fun!
Oh, btw, in the future, if you want to respond to someones answers, instead of creating a new question, you can EDIT the original question and add additional details... :p