I think Jesus chose to appear in this way to his disciples because He wanted to convince them that He was alive and He was with them and that all was not lost.

This was the second time that there was a miraculous catch of fish and this time as the reading goes further, Jesus questions Peter whether he loves Him and when Peter said 'yes', He said 'feed my lamb';  the second time He asked the same question and Peter responded positively - Jesus said 'Take care of my Sheep' and last of all Jesus said 'Feed my sheep'. 

Here we see that Jesus chooses Peter to be the leader of His disciples and instituted the First Church with Peter at the Head.