Getting a KX125 what common problems should I know about

If you can get a newer model that would be the best imho. Find one that is stock w/ little to no wear on it. Check the compression when you buy it and if it is good (and you buy it) change out the spark plug, air filter, fluids, clutch, buy fresh cables (and possibly levers), brake pads and get a new set of handlebars w/ your favorite bend and grips. If it is in the budget get some new tires, tubes and a new chain and go ride!!! Probably looking at about $350-$450 for the parts depending what you get but you will have a fresh bike that you will enjoy. If it does needs a top end (pistons, rings and gaskets) and nothing else factor in about another $100-$150. And once you get some $$$ saved up I would get a Pro Circuit Platinum Series pipe and a PC silencer, V-Force Reed Cage, jet kit and possibly a rear sprocket(s) to alter your final drive gearing for the type of terrain that you will be riding on. If you are in deep sand or loam, tight trails or ride where there is a lot of hills--try to drop down a tooth or two, and if you are on flatter, harder packed surfaces, you can usually get away w/ stock gearing.