Nice to have you join our forum. We always enjoy others that understand the animal overpopulation problem and "common neglect" caused by pet store recommended housing, feeding and care.
There is nothing about the kiddie pool that will harm your new companion. Many people simply choose not to use them as their round shape is hard to fit into the house and their wideness can make it hard to catch them when they run from you.
Also the sides are often taller then our C&C housing and they can't see out quite as well.
If the pool works for you then stick with it. If you decide you want something that fits in your home better, can be built to always be up off the floor and provides loads of options for multiple levels and improvements you will find lots of ideas here on the site and we are here to help if you desire.
Now let's go over what you are feeding. I know you want the best and it can be confusing what to feed so here are the basics your GP should get:
-Plain pellets. No seads, nuts or colored bits. Not only are they too fatty they are a choking hazard. The best brands are Oxbow Cavy Cuisine
Http://oxbowhay.com or KM's Pellets
http://kmshayloft.com
-Unlimited Timothy Hay. Very important for tooth maintainance and gut health
-Fresh Veggies at least a cup a day per GP. There is a great list here for safe veggies
http://www.guinealynx.info/fave.html
-Fresh water. Do not add anything to the water. Vitamin drops are useless and can be dangerous.
-Avoid store bought treats. Seed sticks are unhealthy and dangerous, yogurt drops are not healthy. Your best bet for treats are extra veggies or fruit.