You can manually re-order the attachments by dragging them around. Or you can use a script that re-orders the attachments. However, it can be a little tricky to determine when the automation script should run, especially if attachments are sometimes deleted.
If you are not interested in writing a script, but have budget to hire someone to write the script, you can book an appointment with me to discuss your needs and some of the issues you may need to deal with.
Note that you may want multiple scripts: one to reorder all of your existing attachments, and another script to reorder future attachments. The first script is fairly straightforward for an experienced script writer. The second script is trickier because it depends on your workflow for adding attachments. One option is whenever the attachment field is updated to move the last attachment to the front of the list. However, this is problematic because the value of an attachment field can in other situations that do not involve adding an attachment to the end of the list.