I recommend starting with vim because it concentrates on being a fantastic text editor. I’ve barely used emacs, but people jokingly call it an operating system :~). It’s a monster and it even has an Evil Mode, which supposedly feels like vim. I’ve heard of people who have migrated to emacs because of evil mode. However, if you want to use emacs you should at least be able to read lisp, which is not an easy task for the uninitiated. Vim’s scripting language is arguable not great, but it’s easier to understand what is going on in your .vimrc
Vim (and Emacs) have a learning curve similar to a brick wall. It took me about two months until I felt as productive as before, and another week to feel vastly limited by conventional arrow-keys text editing. And I was already familiar with using the hjkl keys as movement keys, add another month or so if you are not. You should be willing to spend extra time learning vim/emacs and get annoyed often because getting anything done takes ages… until you get it :~)
Edit: I like this image.
