The watt rating refers to the amount of power they can handle. 1/8 watt means that once you get above 1/8 watts, they will start to burn up... 1/4 watt's max is 1/4 watt. Knowing that our voltage is almost always 9v, and the max current we'd have goign through a resistor is maybe 10 mA (though that would be pretty high...) P=IV, or .01*9=.09. 1/8W is .125W so you will be fine with that-same with 1/4W, 1/4W can handle anything 1/8 watt can. So why not just make resistors with really high power handing? (you can get many-watt resistors) Because they get bigger... sometimes very very big. 1/4W are only a little bigger than 1/8W, but are slightly more common, so they are often cheaper, which is why you see them more.
Log refers to the taper pot-if you need a 100k log pot, get one with an "audio" "logarithmic" or "exponential" taper.
In that graph, the rotation amount is plotted against the ratio of the resistances from the middle lug to one side vs to the other side. So a linear pot has a resistance ratio of 50/50 at 12 oclock-so a 100k pot would have resistances 50k from the center lug to either side lug. For a log pot, the ratio is about 10/90, so at 12 oclock a 100k pot would have resistance 10k from the center to one side and 90k from the center to another side.
Know your pots... http://www.geofex.com/Article_Folders/p ... tscret.htm