How does one buy groceries?

The methods my parents used were very mysterious to me, and usually built a collection of edibles that were either filling or tasty or both. I don't understand how they were choosing, but I know it wasn't following any sort of plan other than their own tastes or simplicity of preparation, or cheapness. I'm not too into my food, so I was useless when asked what I would like. I also extremely dislike being in grocery stores or meandering in any store at all, so if I was sent out for groceries I would request a list that I could blindly follow. I would also be back in record time.

Are there certain groceries that it's okay for me to buy online and have shipped to me? Can I at least research online to cross-compare, to avoid having to sit around and make up my mind in-store, or should I expect certain in-store details that are unmentioned on any website? For research, should I use whatever chain (Walmart, Target, Kroger's, Sam's Club, Food City, Big Lots, Dollar General) websites there are, or is there a website that compares across chains for me? I suppose it doesn't have to be as wide of a search as the list of stores I just mentioned.

I do obviously have an interest in cheapness. But I also have an interest in doing as well as I can. I eat nearly no deserts, unless they are offered to me. Edit: Also, desserts. I've never eaten an entire desert before!

There's only about one privately owned grocery store in this town, so I was wanting to visit it after I could compare from the chain stores. It's especially easy to do so because it's usually completely empty of other customers.

Also, the overwhelming number of brands. ...I don't like that. But I don't know how to break it down. I look up "Plain unsweetened yogurt" and I get... that. Confuses the floop out of me.

I don't know what else to ask about, save for serving sizes, food pyramids or whatever, coupons (wasn't there a big post about coupons on Less Wrong?), and volume of purchases, that is, how much I can buy and therefore expand the time between having to shop anew. Edit: In the same vein, preservation. Canned foods, dried, whatever.