How should you predict the battery size required for a project?
Yes, you need to know the average current draw over the period of an hour (or over a period that you then extrapolate to an hour).  That is the mAh (milliamps per hour) that your circuit draws.

It can be hard to calculate the actual current, though, since it is always changing depending on what is actually happening in your system at the time.  So I would suggest picking up a cheap current monitoring USB dongle from eBay / Amazon / Wherever (one with an LCD screen that gives mAh, such as this one and use that to get the total mAh of your system over an hour.

Multiply that mAh by 8 (the number of hours you want it to run for), and that will give you the minimum mAh for your battery. And then add some more as a safety margin, since the capacity of a battery is subject to many things (like temperature, age, etc), and the rated value is only a rough guide.

For instance, if you find your circuit uses on average 387mAh, then a battery of 3600mAh should be adequate.