I've enabled mouse and clipboard and ... something else:
set mouse=a
set clipboard+=autoselect guioptions+=a
That's almost perfect, but I want it so that when I left click it moves the cursor and enters insert mode. I tried this:
set mouse=a
set clipboard+=autoselect guioptions+=a
nnoremap <LeftMouse> i
But then it enters insert mode without moving the cursor.
I'm sure this should be obvious... but I'm just shooting in the dark - true stackoverflow-driven-development style. I have no idea what to even search for.