Nice job Nathan.
Here's a couple of things that might help you out. I'm not exactly sure how you did the selection to create the transparency around the figure, but what you want to do is feather the edges of that selection. This will cause the transparency to fade from fully transparent to fully opaque along the selection boundary. You'll end up with a smoother looking edge that way. I don't use Photoshop, so I'm not exactly sure how you'd feather a selection, but in the GIMP it's under the menu Select->Feather... (of course you must select something first).
Another thing is GIF is an indexed color format, which means that each color in the image is assigned a number and then each pixel is assigned the number of the corresponding color (kind of a paint by numbers for each pixel). The problem is that most color indexed images are restricted to 256 colors for the whole image. This works well for graphics that have simple, limited numbers of color like this smiley
. But, for photographs, indexed colors can make the image look flat. They can also make it look artistic or painterly, if used well, so this can be a tough choice. RGB space image formats like JPEG store the color of each pixel individually as a set of red, green and blue values, so there's no limit to the number of colors in the image (but there is a limit to the number of colors available for a given pixel usually about 16.7million). PNG is an RGB image format that supports transparency (there are others), so you might want to try that. The problem with your white line at the bottom is that those pixels have a different index from the one you selected to be transparent. Most of your white background ended up with the same color index but some of it is a slightly diffent shade of white and thus has a different index. GIF only allows you to select a single index as transparent.
Sorry for babbling on so long. I hope this helps. Feel free to PM/e-mail any questions. I'm happy to help. Good luck.