The resolution shouldn't have anything to do with his white edge problem; however, D13 is correct about using 512x512 resolution (or smaller) for small objects...you may want to consider creating your textrue in it's "true resolution" as well (that is, if the final texture res. for a particular object is 512x512, then create the texture on a 512x512 UV Map), it helps give it a more "crisp" look.
I've ran tests before, and it seems that FPSC will indeed show the textures in 1024x1024; you just end up using more memory than you need to.
-Keith