Well, to me it sounds like the first plant needed to be accustomed to the sun you were giving it. Herbs like basil should get full sun to get the most out of flavor, but if they are not used to it they will be hit hard. It can take a week or two to get them used to it by slowly introducing it to the sun, a little more each day. This is called hardening off the plant.

Even though basil should get full sun (all day sun), they will bolt to seed if they are too hot. Plants in pots get hotter than plants in the ground, because the ground will keep roots cooler. Potted basil that is shaded (like, with shade cloth) will be less likely to bolt. Plants in tiny hot pots often go to seed asap because they think they will die soon.

You probably should not water everyday unless it's a tiny pot that dries out every day, and if that is the case will probably want to get a bigger pot soon, so that things are more stable. The more soil capacity, the more stable the temperature and moisture. Push your finger into the soil, and if it's moist you do not need to water it. Depending on how hot it is, you may need to water it more or less. You can also pick up the pot to see how heavy it is. A completely dry pot will weigh less.

Basil is an annual plant that is easily started from seed. You may want to let one of your basil go to seed so that you can try it again next summer.

It is a very small container, imo, and it drains fast. I have been sticking my finger into the soil and the top inch or so is usually dry. Not bone dry, but not moist. I did have the plant in the shade for the first couple of days because I thought I was going to repot it right away, but it started to droop right away so I was worried it wasn't getting enough sun and moved it. My biggest pot turned out not to be big enough and I didn't want to damage the roots. I plan to repot ASAP. I work at Goodwill so I have been waiting to see if we get one big enough in, otherwise I will get one next week when I visit the nursery. Like you said, it is trying to go to seed, I pick buds off of it pretty much daily, so I'm sure it's not happy about the container it's in. Thank you for your advice.

At the nursery, you might as well start with a new plant that is easier to take care of. Have you considered trying with a hardy perennial herb like thyme? If you live in USDA zone 7 or warmer, rosemary is super easy. Basil is a plant that doesn't live long and when you buy it at the grocery store, its purpose is to eat it as it won't really produce much more than you are buying.

Basil starts very easily from seeds.