Here is my approach for keeping my starter happy with minimal discard. This assumes you have an active sourdough culture.

I bake once a week, and keep my starter in the fridge when not making bread. I find that keeping a stiff starter in the fridge keeps it healthy for the next baking session.

I found through trial and error that you really do need to do at least 2 feedings of your starter after it was in the fridge, otherwise it's activity declines over time.

Starter

Get started on this a full 24 hours before you mix your dough. You want to do 2 feedings before using the starter.

Do the first feeding the morning of the day before you will bake. When I pull my starter from the fridge, it looks like this.

Mix this up and let it sit covered on the counter all day. It will double in size by evening, eventually looking like this.

Do the second feeding the evening before you will bake:

Mix this up and let it sit covered on the counter overnight. It will double in size by morning, eventually looking like this.

I like to use a 50/50 mix of whole wheat flour and bread flour for each feeding.

You can use the remaining first feeding starter as discard. I like to use it for a batch of pita bread.

You will pull 100g of the second feeding starter into your bread and have a small amount left to save. Mix in equal amounts of bread and wheat flour, enough to make a stiff ball the texture of playdough. Let this sit in a covered container on the counter for 4(ish) hours, then put it into the fridge.

I keep my starter in a small mason jar in the fridge.

When you want revive this starter ball for your next baking session you will likely use about half of it. Over time you will end up with a couple of starter balls in your fridge. Throw the older one away every few weeks. Do not put it down the drain, it will definitely turn to cement and clog up the drain.