How about....... duplicate your image, then insert a blank layer in between the background and its copy. Delete the Background Layer. You should now have two layers - a transparent one at the bottom and the "background copy" on top.
Now, using the Magic Wand or the Selection Brush, select the background of the image - or anything else you don't want to keep. Add a small amount of Feathering. Now, on the top layer, either go for the Eraser and wipe over the image (no need to be accurate, you'll only remove the bits you don't want) OR just cut the selection (Ctrl-X).
Now, in the layers palette, right click on the top layer and select "Merge Down". You should now have your subject on a transparent background, in one layer.
Now go to File > Save for Web... and choose PNG-8 or PNG-24, and check the "transparency" box. It will be a big file, but can be altered to a suitable size for the web - which is really what PNG is for. This was what I got...... (and obviously missed a few pixels at the bottom)