2003 will give slightly more power. Wiring your two 16ohm speakers will actually allow your amp to output a bit more power since it will see less resistance.
Yep two 16Ohm in parallel is 8 ohms.
The datasheet has a decent little circuit on it and if you have the parts its worth a try and will probably sound great. If you are only going with what you have on hand you might be getting a junky sound depending on what parts are of what quality.
Try using some paper in oil caps or polypropylene for low values and Panasonic FC series of electrolytics for high values. Use Dale RN55 series resistors (metal film) rather than carbon comp. Dont use ceramic caps at all.
Page 6 and 8 of the 2003 datasheet are going to be the most important to you. They include the circuit and the bill of materials.
To purchase the bill of materials with the type of parts I suggested you could spend as little as 10 dollars for stereo, but I think you are doing mono so cut that in half. Its hard to buy Paper in Oil piece by piece so if you were to use those (the sound nice and smooth) your price would go up by probably $20 for 10 of them on ebay shipped from Russia or somewhere near there.
You always have to up the power to get more volume. Just figure that your circuit will probably be 60% efficient or to make it real easy figure 50%. Take the voltage of your battery and multiply it by the maH (milliamp hours) and divide by one thousand. That gives you the watts you can push into the amp from that battery in one hour before the battery dies. Now divide that number by 2 and you get approximately the wattage your amp will push.
You could pack a 50 watts into that lunchbox if you wanted. I dont know how many watts you want but I am sure you could get whatever you need to fit in it. But then you need to build a power supply and we get to around $2 per watt and maybe $3.
If those 16Ohm speakers are identical I would run them in parallel. It will be louder. If they are not identical its to easy to try both anyway. Why not? Your are not risking hurting the speakers and all it takes is two pieces of wire.
Dont worry about being a newb, this is the place for newbs like you and like me

Ri