New to hiking, current routes of 2-4 mile hikes because i am not in shape to do much longer hikes

Went to a local 3 mile hiking trail that was pretty high elevation with a lot of rocks and water from a creek that runs through the trail and about slipped multiple times

almost everyone I saw on the trail were using hiking sticks

What brands should I look into for foot wear, and are hiking sticks really important to use?