You don't have to choose "Save for web and devices." Choose "Save as..." and then there will be a drop-down near the place to enter the file name. Select one of the options like png, jpeg, or other wise. Just be sure you save another copy of the image as a psd so that you can use it for some...
It might also be that you saved it as a PSD. Considering that you have a brand new copy of Photoshop, you might not be doing the final step to save it as a PNG/JPEG/whatever. A PSD is a save file of all of your Photoshop work so that you can go back and edit it later, without having to redo the...
I'd also like to add that if you have any questions on the creation of avatars and signatures, you can take a look at our new graphics resources thread. There is a ton of information there that will help with the improvement of your graphics capabilities.