I had a sourdough starter back in the day, more recently (until I had to give up baking due to my diabetes) I had a "Herman" that is a sweet dough starter.
I used a heavy plastic container that originally was a half gallon of locally produced ice cream. It was opaque but I could see the level through it. I believe in non-metal containers and utensils with my active foods, so glass and plastic or wood for stirring. It fit well on top of my stack of dinner dishes in the cupboard, in my temperate climate that was the best place for it, but out of the light. Being on top of my plates meant I had to be aware of it. You want to have at least 2-3 times as much space as starter you wish to keep.
My starter required attention about every 3 days, whether to feed or stir or use. When I wasn't baking a lot, I only fed it small amounts, tablespoons instead of cup portions. If you get more than you want to keep, just throw some of it out! Or bake, the real answer is to use it.