Well normally the battery sitting might give out over 12 volts while car isn't running and once the engine is being turned over it drop but if a good battery the current would go right back up once car is started. You have to also test the alternators input it should be the same voltage you find the battery at once engine is off , the alternators output voltage shouldn't really be much higher then 13.8 volts ever but if faulty alternator the alternator could give out either low or no voltages or too high.
Another thing is what the battery is rated at , example the battery is a 12volt car battery and side or top mount but it also has a cold cranking amp rating too. It's best to use a high cranking amp like at least 750 or 850 cold cranking amps especially if the climate has cold and hot temperature extremes.Interstate battery's are I find excellent if you ever need to buy a replacement battery by the way and offer a great cold cranking rate like 750 ot 850 or more depending on price range you choice but a basic battery from them goes for about 90 bucks is rated high in cranking amps and has a 5 yr warranty.
Hope that helps and best of luck.By the way a voltage meter , 12volt lite test probe and a good service manual would help you out here but also you could phone around and find a shop that offers free charging system and battery checks.