Li-ion batteries are dangerous, but they do hold the max charge/weight of any type of battery. Though the "take the circuit board from a used laptop battery" initially sounds like a good idea, BE CAREFUL. There are actually two types of Li-ion batteries, 4.1V types and 4.2V types. Linear Tech makes a line of Li-ion chargers. Basically, you charge at a constant (max) current until the voltage reaches the max (either 4.1 or 4.2), then supply constant voltage until the charge trickles down to 20% of max current. At this point the battery is considered fully charged. Also note, a Li-ion battery is considered fully discharged at 2.5V... if you fully drain one below this level, charging it again could cause it to EXPLODE (our first R&D fire)... the battery manufacturers test them in a bunker type arrangement. We applied for and received a patent for the way we monitored our 4 stack battery charger, and shut the battery down if any cell went below 2.5V, not just the stack going below 10V... so, if the dead Laptop battery has six cells in it, don't use the board to try and charge 2, 4, or even 6 if they aren't the same type and flavor as what the original batteries were.
Now, for battery capacity... very difficult problem. Voltage in no way reflects remaining capacity. It changes with: temperature, age, load, battery type, battery size. The only way to know how much charge remains is by accumulating what went in, and subtracting what came out... hence the line of fuel gauge chips. There just is no easier way, especially if you're using it while you're charging it.