Samsung galaxy S3 GT-I9300 4.3 Jelly Bean to 5.0-lollipop
Yes, it's a good idea.  
Yes, your phone will support it. I've seen ROMs for the S3 (i9300) up to 5.0.2.  
Benefits include: security fixes, better stability, improved battery life, new features and a lot more!


To update your phone, I would suggest 


rooting it (there's a lot of information on rooting over at the XDA Developers Forum,
flashing a custom recovery like CWM, and
installing a custom 5.0.2 ROM. There are lots of them on XDA, so I'd spend a little time having a read up on the various functionality available.


As for why your friend got the update: it's possible that he has flashed a custom 5.0.0+ ROM also.