Needles (sharps) and thread of course, a thimble (metal or plastic - there are several different types), a small pair of scissors, an emery grain filled pin cushion (to hold needles and keep them sharp), maybe some beeswax (to keep thread from tangling and knotting while you are sewing). I can't think of anything else without going through my sewing box.
Depending on your eyesight, maybe a needle threader to help you thread the needles. And a small box or basket to store your things in. I have a small plastic box I got at the dollar store. It has compartments so I can put my thread in one, my needles, thimble, scissors, etc. in their own sections.
I am not sure how readily available it is in stores, but a member here sells it on her site. www.NAKPUNAR.etsy.com
you might want to take a look at her site. She also makes and sells her own pincushions filled with it.
You are right about starting out simple. If you want to sew garments, get patterns such as: Simplicity-with the word Easy upon the front of the envelope; Kwik sew-easy; Mcalls-easy. Basically, look for patterns with emphasis of the word "easy" on them to start. If you have a sewing machine, or looking to buy one, buy one with basic stitch functions. If you go to a dealer to buy one, alot of times they will give you a class or two on how to use a machine for free. If you want to buy a used one, look in either in your local classified-ads. On-line, try Craigslist or Ebay. With a used one, make sure it works-find someone who knows to show you if it works. Also, if that person is really good at using a sewing machine, or knows the basics of how to use one, have them show how to do so for free. If you can't findsome, check the local school districts for adult community education courses, because sometimes they have sewing classes for a reasonable fee. Churches also sometimes have monthly sewing/quilting classes as well and there is a place to check and see as well. This web-site has some decent video tutorials on anyother skills that you need once you get the basics down.