Excellent advice again
Like whats been said, don't get hung up over saving.
I didn't have that much at the time of application so, my wife did a very good cover letter explaining why eg...numerous trips back and forth etc etc.
Like what Terpe said you just got to show that after all bills and living cost you have enough to live on.
Jane did a list for them...making it as easy as possible for them to see that we are indeed in control of your finances and that the books do balance.
That's really all they are looking for. Like you rightly said ' you wont be a burden'.
Also your colleagues are correct, the paperwork is simply as long as you have all documents they require.