Welcome to TFP! First and foremost, Ignore Leslie's. They have a sales goal to make and all you are to them is a boost in sales! Secondly, invest in a good test kit. I'm not talking about test strips either. Consider the TF100 test kit. It's the one we will recommend to you as it offers accurate testing at an affordable price. Thirdly, please read Pool School. The link is on the upper right hand corner of this site.
Inside, you will find all the information you need to keep your pool sparkly clear. Now I will see that you definitely don't have enough chlorine. Before we get to that, you need to ensure your CYA(stabilizer/conditioner) level is adequate. You should aim for 30-40 on the scale. Seems you have 60 according to Leslie's, but there's no telling how accurate their testing is. Without a proper test kit we are taking a shot in the dark.
Back on topic, ensure your CYA level is adequate. Next, check your PH and alkalinity levels. Alkalinity acts as a buffer. Keeps your PH in check so adjust it first. Always remember that chlorine is a fantastic oxidizer but you have to replenish it. We don't recommend you use "shocking" powders to chlorinate your pool or chlorine tablets. Both add chemicals to your pool that you either don't want too much of, or don't need in general. Household bleach(regular kind not flavored) has the same active ingredient as liquid chlorine that you would find at the pool store.
With that in mind, you can use bleach to chlorinate your pool! That opens this up to what we like to call the "BBB" method of taking care of your pool. There is a lot of information in Pool School, but as a short summary you will be using Bleach, Baking Soda, and Borax in place of expensive pool store versions that are literally the same ingredients as PH up and alkalinity up. Not only will using this method be easier, but a lot cheaper as well.
Using this method, you will use of course Bleach in place of tablets or powders, baking soda in place of alkalinity up, and borax in place of PH up. Like I said, pool school has all the information you will need to make your pool care a lot easier.