We had a guy in our league bowl all year and barely average 100, he didn't fit in our league.
At 150, you should be fine to join any league except the ultra competitive scratch leagues. Another reason not to worry is that in general, summer leagues are less competitive than the winter leagues.
A couple years ago a pair of brothers joined our league, neither had ever bowled in a league before, both started around 140-150, by the end brother 1 was up to 170, brother 2 was over 180.
Stay away from junior leagues. You'll probably be at least 2 years older than the next oldest bowler. Go adult so you can have a beer or two while you bowl.
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What are you gonna do? Beat me with your Jesus stick?