Use the command
vim "+norm Go" "+startinsert" $filename
to automatically move at the end of the file and start editing.
This is useful when you are invoking vim from another script i.e. when you don't want this to be the default behaviour but want it in a special case.
For me this was useful for my journal script which appends the current time
at the end of a file and opens the file and (now) automatically moves to the end
and goes to insert mode.