What is the best way to keep the sourdough starter?

The reason you throw out 1/2 the starter is because it can outgrow its container (and make quite a mess in your fridge). So you don't need to do this every time - keep the starter at about the halfway mark for the container and you're good.

Best way is hard to answer. It's very much a matter of personal preference, your cultural tradition, what flavours you are going for... and so much more.

This is a great article about keeping a starter: http://food52.com/blog/5327-maintaining-a-sourdough-starter If you are just looking for a simple, easy to follow, well written guide, don't read the rest of what I write here.

Although, to be honest, I completely disagree with it. Cooking with sourdough does not need fancy measurements, precise ratios, kitchen scales...unless you are a professional baker or cook. People have been successfully baking with sourdough for a few thousand years without digital scales. I do a lot of historical cooking (re-enactment cooking) so I prefer to use methods closer to what the pioneers heading West would have done. I keep a very small (about 3/4 cup total) very, very thick rye starter. I use it to make a sponge, and how thick or thin I make the sponge will influence the final texture and sourness of the bread. I keep this kind of starter for several reasons, but most of all because it takes up less space in the fridge.

The booklet Baking with Sourdough goes into way more detail about how you can influence the rise and flavour with the texture of your starter/sponge: http://www.amazon.com/gp/product/B001RNNBAK/ref=as_li_qf_sp_asin_tl?ie=UTF8&camp=1789&creative=9325&creativeASIN=B001RNNBAK&linkCode=as2&tag=adveofawholwh-20

I keep my starter in a mason jar in the fridge. I feed it once every week or two. If you keep it on the counter, you'll need to fee it daily.