How do I get out a stuck spark plug? Should the size or "thickness: of the socket itself be a concern?

if you can get a good socket on it try /use a impack wrench...

Even with a right size socket and a long wrench? It should not be that hard... Personally, I would advise not using the impact for this application. You should have enough grip with the long wrench. If it still doesn't work, you can loosen it up with an extracting socket if you find one that is deep enough. It'll ruin the spark plug but I suppose you want to change it anyway. Should look like this http://espimages.biz/2386/I/131/362/ST38306.jpg