My experience after several summer trips to the Disney waterparks:
We never rent towels. You really cant carry your towel around with you and being wet from attraction to attraction is not a big deal. Really the only time you need it is when you ready to leave to dry off before changing. In the summer you dry off pretty fast without a towel.
We rarely get a locker only times when we are coming from a theme park and have things we dont want to leave out. After that, my advice is to not bring anything valuable to the park and just leave your t-shirts / shorts and flip flops at a chair.
We never wear pool shoes/flip flops/
crocs or anything similar around the park. Disney is one of the few water parks I have been to that sprays water on the paths so it is very easy to get around without burning your bare feet.
Wear sunscreen. Goes without saying
We dont get chairs and umbrellas. I dont look at the water parks as a place to lounge. There are so many people!! I would do that at your resort pool not the water park. If you feel like relaxing, try the lazy river!!
To ride the rides, early AM (like every other park) is the best time to go - especially if they have EMH. The difference is there are no fastpasses so if you go later, you will wait for most of the headline rides. But they do move pretty fast.
Be careful of weather if you are planning to go later in the day. We do this often when we are at the parks in the AM then plan to go to the waterparks in the afternoon. If there are typical afternoon thunderstorms in the area, they will close down the attractions until the thunder/lightning clears. That can be a real bummer!!
A few people commented on the wave pool at TL. To add to the strong waves, be aware of the cement bottom. You will forget it is not sandy and soft like the ocean and you will scratch/cut yourself if a wave knocks you over.
We usually do the water parks for 1-2 hours at a clip. We go, we do a bunch of slides, lazy river, wave pool, etc then leave. I cant imagine doing a whole day there. I guess if you are paying for a full day, it makes more sense. We usually have the special DVC premium APs so the waterparks are included.
If you have tweens/pre teens - The ski patrol section is blizzard beach is unique and a ton of fun and pretty cool that there is a "play section" for older kids.
Have fun!!