You tend to see pictures of sourdough starters in big jars. But you don't need a big jar! A tiny amount of starter is enough to get going.
Each time you feed it, the size multiplies, so you can start with a teaspoon of starter and make enough for a big loaf in just a day or two. When I'm in a bread-making routine, I keep like 10g of starter. One feed brings it up to ~50g, another feed to ~150, and that's enough for a loaf (saving 10g for next time).
If you keep your starter in a big jar, it'll just go to waste. Keep it small and you'll never need to throw any away.
On more than one occasion, I've made sourdough pancakes or something, and forgotten to save some of the starter. The tiniest scraping of uncooked batter from a leftover spoon is enough to keep it going -- just mix it with flour and water and the magic happens.