As far as photographing and documentation, there is not much you can do to speed up the photographing process. I recommend photographing not only the outside of the computer and all the identification labels and markings, but also photographing the inside of the computer. Take pictures of any and all damage inside and out. Photograph the HDD/SSD in place, and after removing the HDD/SSD photograph it from all sides and identifying labels. Photograph any optical discs, flash drives, sdCards, etc. that are in the computer or connected to it.
As far as speeding up documentation, I recommend using a fill in the blank form. This form should have boxes for make, model of the computer, serial number, peripherals, and so on. This form should also include space for the HDD/SSD make, model, serial number, size as reported on the label, and so on. You can include in this form spaces for the software you used, the version of the software, if it has been processed, and if any searches were done. This will also help your coworkers know what has and has not been done quickly in case you are not able to be reached to answer any questions.
It may sound like a lot, but once you have the form and know the flow of the form, you will be able to fill out quickly. It will also assist you with getting the information you need and not forgetting something.