As I’m growing my starter I am storing it in the oven as that probably has the most consistent temperature. Is that OK, or would it do better on the counter top? Thanks!
Frequency of use is a convenient way to determine where you store your starter. If you plan on baking everyday, then somewhere that is convenient and not subject to accidental jostling by energetic children, rowdy teenagers, or an inquisitive cat would be ideal. Daily refreshing should keep the starter active and dependable so unless you're kitchen temperature drops precipitously at night, a few degrees variation won't hurt.
On the other hand, if you plan on baking every few days or on an irregular schedule, you can keep some of your starter in the fridge and build a levain for the different loafs as needed. I work with about 50 g of starter at a 65-75% hydration kept in an airtight container and use 20 g at most to start my build. When I get low, I design my build to leave an extra 50 g or so. I can easily go two weeks without baking and with a three step build, have a vigorous supply again. It does take some time management awareness but it also saves a lot of flour and discarding excess starter.
I'm not the only person here that does this or uses a similar method.
Check out this link.