To start with a conundrum, Stiff or Wet?
I've noticed that a few recipes entail using a stiff or wet starter. I am on my third starter. The very first, I threw out too early believing the odor to be indicative of rot. The second I ignored the odor and made a delicious sandwich bread but failed to hold back any starter to feed into the next week. The third starter, I doubled and doubled down on the recipe to ensure I had enough to carry on after I made my weekly bread. My starter seems to be a dough of sorts, so I assume I have a stiff starter. Looking back at the sandwich bread I made last week, I had to add more and more water to make the dough less crumbly and more kneadable. So, since I may have figured out how to make a stiff starter, then how would I make a wet starter? Why would I prefer one starter, stiff or wet, over another?
If you want extensive and scientific discussion on the topic of firm and liquid starters and the flavor profiles that they bring to bread, let me suggest that you use the search feature on these pages and put in "Debra Wink".
Beyond the discussions of acetic versus lactic flavors and high and low temperatures, let me discuss simpler bread baking matters.
Many folks prefer to keep a storage starter at a certain hydration and for baking, create a pre ferment that will have the characteristics that we need. In this way, we can have the correct hydration for our baking purposes without keeping multiple starters. (Or accidentally baking our starter.)
In general, a liquid pre ferment (and you can create this by taking a small amount of storage starter of any hydration and building a pre ferment of equal weights flour and water) will - because of the increased protease action - bring an extra extensibility to the dough. If you wanted to make sourdough baguettes, you would almost certainly use a liquid levain as a pre ferment.
A firmer pre ferment will bring acidity to the dough without the high protease action. This will strengthen the dough - particularly when sourdough is used. A baker might use this with a weaker flour, or when extra strength is desired in the dough. If you are baking with lower protein wheat (or my bete noir - triticale) you would want to use a firm pre ferment.
As for the hydration of the storage starter, the impact on the flavor profile of hydration and temperature are quite complex. Your maintenance routine will have impact potentially beyond that of just hydration.
I keep a liquid starter (100% hydration - or equal amounts by weight of flour and water) because I feed my storage starter daily and the math is easier this way. It has also developed a flavor profile that I like (pretty mild) and I want to keep it that way, so I do not vary my maintenance routine. When I want a firm levain I simply use a bit of the 100% storage starter as a seed and build up the levain to be used in my formula.
As for baking with your starter, let me once again commend www.bbga.org - look under the menu option "Bread" and read the "formula formatting" article. Understanding the fundamentals of a formula (and overall hydration and percent of flour pre fermented are two biggies) will provide you with a decent foundation from which you can explore.
Hope this helps.