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Leave it at room temp. The yeast bacteria will develop/thrive at room temp if you start and feed it at room temp. It will act slightly differently as room temp changes tho. Many bakeries have trouble with their starters as seasonal temperatures change. And getting a consistent sourdough is reliant on getting consistency with your starter, and that consistency will make trouble shooting easier too.
You can refrigerate if you're not going to be using it for a few weeks, and then to prepare for use again simply take it out and start feeding it for a few days and it will become active. Depends how often you're going to be using it, but I'd say keep it out as long as you're feeding it. Once it's established, you can also reduce the feeding schedule if you're not planning on using it.
Add 100g of flour to 100g of room temp water in a tupperware/kilner jar/jam jar. Mix and leave lid ajar. Add flour and water in equal proportion each day, 10-25g of each, and stir in, leaving lid ajar.
After a few days you should have bubbles. If the jar is too full, empty some out before you do your daily top up. You're trying to get activity in the mix, so you're not really losing anything by throwing excess away. You should have enough activity after a week or so. When the mix is bubbly, drop some in water - if it floats, this is a sign that it's sufficiently active for use in baking.
This is my new starter on day 3.