It can be tempting to pick up your local classifieds and simply choose the lowest price laptop in the newspaper and buy it from whomever. This is a mistake. Less headache and aggravation will result by buying from a reputable dealer. If something goes wrong with it right after you buy it, you'll at least have some recourse.
Laptop batteries generally don't maintain a full charge for more than a year or two at most. The manufacture date of the laptop is often found on its underside. If the manufacture date is more than two years and it has an original battery, consider yourself lucky with any battery life you get. Most used computer dealers will not give you any warranty for the battery. An extra battery is always a wise purchase when buying a used laptop. Consider asking the dealer what it would cost to get another one.
Sound and video are both things that are important to some people and not to others. If you see yourself listening to music using the laptop speakers, try to play some music on them to see how they sound. You may want to cart a music CD with you along with your Knoppix CD. Have realistic expectations though. Laptop speakers rarely sound full. They usually have a tinny sound with lots of treble and little bass.
If you plan on watching movies on the laptop, you may want to consider choosing a used laptop computer with a DVD-ROM drive in it. If that is important to you, I would suggest you carry a DVD movie with you to evaluate how well the laptop plays back video. If it pauses and labors with the DVD, you may want to consider another laptop.