I either made them fresh or made with hot water, cooled quickly and stored in the fridge (usually for the overnight ones). During the day, making them fresh was usually easiest, it saved having to make them, cool them all and then re-heat. We didn't really switch to formula until 10 weeks, so by then it was easy to predict roughly when she would likely be hungry, so I would boil the kettle 20-30 minutes before I planned to make the bottle and then they are fine at room temp for 2 hours before you need to discard them, so I knew she would always want it at some point before it got too old.
For the overnight ones when I didn't have the luxury of doing that, in the evening before bed, I would do the same, boil the kettle, leave for 20-30 minutes, then make a set of bottles for overnight and the first morning one, set them in a big bowl of ice water to quickly chill then store in the fridge and warm in a bowl of boiled hot water as needed.
You definitely shouldn't use room temp water to make the bottles as it needs to be hot when it first comes in contact with the formula powder in order to sterilise it. The idea is that you boil the water not to sterilise the water or the bottle, but the actual formula, so it needs to be hot when you make it. It is less ideal to store them in the fridge for use later because it can risk bacterial growth, especially if your fridge isn't clean and you aren't good about keeping raw meats or things far away from where you'd store the bottles, so cross contamination is one concern. But I think also some people just make the bottles hot and shove them in the fridge, but you actually need to rapidly cool them to a point below like room temp pretty quickly because there is a temperature range that really encourages bacterial growth in milk products, and it can take a long time to cool just sitting in the fridge. So it ends up just being like feeding a bottle you've left out sitting on the counter for 8 hours, which can be dangerous if bacteria has been able to grow.
I think basically just be sensible. If you're going to make them in advance, just do it with hot water and then cool them quickly in ice and water and put in the fridge right away so they stay cold until you need them. Then just don't leave them in there forever. I always made sure I used the refrigerated ones within 8-12 hours.