Contacts, then eyelashes. My reason is because when I put my contacts in, I usually tear up and my lashes get wet. If you put on false lashes and they get wet, they will fall off right then and there, or soon after.
*Also, a tip for putting on falsies: make sure the glue is a bit tacky before placing them on your lash line. If you wait about 30 seconds, you may be less likely to get glue all over the place. Just a suggestion ^_^v