the beginner's league is a lot of fun and will help you get your feet wet as it pertains to playing in a competitive situation.
some people do well, some people don't do so well when it comes time to actually record the scores for posterity.
however, if you're shooting high 50's - low 60's at WW, those scores are pretty darn good. if you can repeat those scores at leagues, you will compete in the amateur divisions and you'll get to meet a lot of cool and like-minded golf addicts such as yourself.
i even have a favorite new players league memory: i came to the 18th hole at +1 for the round. #18 that day was set on the 2nd pin, middle of the tennis courts. my only thought was to get through the first tree gap and not flip the disc over. nice low teebird off the tee out into the field for a 120+ foot upshot for the safe up and down and what would've been my best round ever (league or casual). lo and behold my hyzer upshot with a medium 175 wizard slammed the middle of the chains for an improbable deuce that i still haven't repeated. to cap it all off, it would prove to be my 1st Bag Tag victory; i gained tag #40 from steve harris. my 1st round of par or better! not such a big deal, but man, can golf make you come back for more!