I've had New Hampshires, Easter Eggers, banties, a few crossbreeds--they all love to hunt bugs of all kinds amid tall weeds and under
trees, which is where ticks tend to be found. For what it's worth, breeds known for laying high numbers of eggs tend to be more active/noisier, while meat breeds tend to be least active/quieter but many need extra feed as they've been bred or hybridized to grow faster than normal. Consider splitting the difference with an old fashioned dual purpose breed. More than
enough eggs for the average person, will raise at least a few of their own chicks with extra cockerels being good eating, and eat plenty of the bugs that bug you.
And for what it's worth, most of mine were originally hatchery chicks, but all very quickly picked up on their own that bugs were good eating.