I would like help on how to know which baking pan to use if the recipe does not specify. I have tried measuring the pan using water to ascertain the quantity but it did not help.
First, for the pan type: If the recipe didn't specify, don't use a special pan like a bundt or similar. Take a standard round pan from thin metal. Line with parchment and oil the walls, you never know how much a new recipe will stick.
As for the size, if the author didn't specify, then the recipe is probably intended for the most common size in the author's culture. The first pan to try would be the one common in the place the recipe comes from. This would be a 9 inch pan in the US and a 26 cm pan in continental Europe. I don't know what the standard size is in other places.
After you have made the batter, fill it into the pan. A good upper limit for rising would be 3 times the original height. If your batter takes up less than 1/3 of the pan height, you can bake it. In the worst case, it will go a little bit above the rim, but this will happen so late that it will be set enough to not get a muffin top, and definitely no spillage. If it is more than 1/3 of the height, move batter into a bigger pan.
If a recipe regularly rises much above 1/3, it is probably overleavened. An overleavened cake might look nicely fluffy at a first glance, but it will have problems such as frequent doming and a metallic taste from too much baking powder. You will get better results if you reduce the baking powder.