Look at it this way: if you enter all your times now, sure you'll be low ranked
(but you're FAR from being last, right?) and then you improve them little by
little and you'll see yourself going up ranks, which should motivate you.

Now if you only keep the best ranks, what you'll have is an artificial global
ranking, not representing your true rank, is this what you want?
What's the fun in this? You won't even want to play anymore if you know you're
adding worse times and risk going down.