Hi Nicholas, and welcome to the forum!
If you can define what the loads are, you are a couple steps in already, and you are at a good point to examine power sources and drivers. There is no 'right' way to proceed from here. There are many paths that will get you to your final destination.
You could estimate the size and cost of a supercapacitor bank that would provide the necessary performance, and weigh that against a Li-Ion pack for the same performance. Consider that caps can be charged very rapidly, but the energy density is a lot lower. You'd want to consider the life expectancy, and the operating environment.
Or you could start with the drivers, and let that guide your power source choice.
Or you could start with an idea of what the finished product is to look like, and let that guide other choices.
Most likely, you will find that you end up doing at least the very early parts of many designs, and comparing before making your final choices.
We can help you with those, but we'll need a lot more information about what you are trying to accomplish. The more you can share the more we can help you.