I recommend test fitting before actually ordering parts. This helps me be more confident that they will fit and you know where they will roughly go. This step is optional, but it can save you time and money later.
This is another exercise in which you can use paper and a pen, or an app such as DrawIO on the internet. First, I find the dimensions for all the parts. Here is a screenshot from Amazon showing how to spot product dimensions:
Some information digging is needed to find these for your parts. For each, first find a shop you can buy them at, such as Amazon, a number of online shops, or eBay. You can then search for, or ask for information about, the dimensions of each board or item. Make sure you are looking at the dimensions of the part and not its packaging. The next diagram shows a datasheet for a battery box and...