When I went - we were just going from slide to slide to wave pool to slide, etc - so we never had any "down time" just sitting in a chair watching the world go by. BECAUSE that's how we handled the water park - we put ONE towel from our resort room in a locker with our ID's, tickets, money, car keys, and a change of clothes for me. That towel was so I could dry off to change into clothes when we left. My boyfriend decided that since we were going on a hot day - he was just going to drip dry..... (and he wasn't changing out of his swim trunks until we got cleaned up at the hotel again). But - we could have fit a second towel and clothes for him in a small locker!
So - if you are going to make a full day of it - hang out on chairs, eat food, establish a "spot" that is yours to return to - towels might make sense - and I recommend renting them. But if you are just going to slide hop - there's no place to leave a towel but a locker - and then I would suggesting bringing a towel from your hotel room to store in a locker if you want.
Now - if you don't want a locker or have one person watching your stuff - someone will need a lanyard to carry your tickets, money, whatever. We saw folks walking into the parks from their cars in swimsuits and bare feet. Clearly they had no interest in paying for a locker or having one person watch their stuff!