Getting Started
If you're considering getting into painting, the vast array of supplies out there can be intimidating. I learned by trial and error what I needed, and I want to share my advice. When I was a preteen, I started out painting on cardboard boxes and buying one tube of paint at a time with my babysitting money, so I know what is and isn't necessary when starting out on a budget. This is a bare basics list of what you need to buy to get started with acrylic painting. Click on the links to see more detailed guides on purchasing these items.
Essentials for Starting Out
1) A painting surface ($1-$5 each)
2) Student quality paints in primary colors (~$20 total)
3) A brush or two (~$10)
Extras from home:
1) Masking tape
2) Old shirt or apron to protect your clothes
3) Jar for paint water
4) Old plate for a palette
5) Piece of cloth to roll your brushes in when not in use
These were the only items I used for many years, and I was able to get good results without all the bells and whistles.
Next Steps
If you decide you like painting, there are some intermediate extras I recommend:
1) A few extra colors of paint
2) A brush washer tub
3) Disposable palette paper or a Sta-Wet sponge palette
4) A tube wringer
Things you don't need right away:
Easel: You'll feel more like an artiste with an easel, but for paintings smaller than about 11 x 14, a regular desk or table (covered with newspaper or a drop cloth) works fine. Many beginners find it easier to try flat first. Once you get serious about painting, then it's time to invest in an easel.
Brush storage case: I have bought several brush holders since they looked so neat in the store, but in reality they're bulky, don't stand up properly and are generally unnecessary. When you have only a few brushes, you can store and transport them just as well by rolling them up gently in a piece of cloth and securing with an elastic band. Cutoff pant legs or some other stiff cloth works really well for this if you cut the material a little longer than your brushes to protect the ends. Just don't leave your brushes in the water jug.
Art caddy: Same goes for the special artist's caddy/toolbin things. They look cool, but in my experience aren't really any better than a normal toolbox/tackle box from a hardware store, they have cheaper hinges, and they cost more. If you need to transport your paint, buy a toolbox instead.
Special easel lights: Although I've never bought one (and I would welcome comments from artists who have) I'm not convinced that genuine easel lights are really necessary, since they don't seem any different from hardware-store or Ikea-type task lights with a daylight compact flourescent bulb. Your painting is going to be displayed indoors, not outdoors, so indoor light should be fine, right? Am I missing something? Just make sure your area is well lit enough to prevent eyestrain, and make sure to stop occasionally and check the painting in the indoor light where it will be displayed.