Note: This answer goes in a bit more detail than necessary to answer the question. If you truly only care about the hydration, please only read "Water/flour ratio" and "Flavor of the bread". I have added the other information as well since the effects are similar to that of a change in hydration.
I've frequently baked (about once to twice a week) with sourdough for 4 years now. I'm not a professional. The only thing I can take a bit of pride in is that a professional baker who tested a loaf of my sourdough bread told me that it's "fantastic, considering the little possibilities available to control the conditions the sourdough and loaf are exposed to at home". So while far from perfect, I'd consider my sourdough breads and knowledge pretty good.
Most of what I'm writing now was first read on the internet somewhere and confirmed through testing it with my own sourdough culture (I'm still using the same one I started out with).
Apart from the flour you use, there are several factors that affect the taste of the resulting bread:
Temperature
This has, in my experience, the biggest impact on the taste. The following rules apply:
Anything over 40°C is deadly to the microbes in your sourdough.
Lower temperature: More acetic acid, less lactic acid, yeasts develop more slowly.
Higher temperature: More lactic acid, less acetic acid, yeasts develop more quickly.
Lactic acid bacteria prefer temperatures at around 30-35°C
Yeasts like temperatures around 25°C best
Note: Your sourdough can be 1-2°C warmer than the environment due to microbial activity. That can be important to keep in mind.
Water/flour ratio
Most of the time, people use a ratio of 1:1 water/flour for the sourdough and that will give you good results, but you can play around with that ratio to change the taste to your liking:
Lower water content causes more acetic acid production and less developed yeasts
Higher water content will make it easier for the yeasts to grow and increase the lactic acid content
I've found that having more than 1.5 times the amount of water compared to the flour will hardly have any effect on the dough anymore and I'd recommend stirring the dough every couple of hours with that much water.
On single staged sourdough, using less than 0.75 times the water compared to the flour is also not a good idea and you will probably be required to add yeast in the bread dough.
Salt and oil
Adding these, especially salt, to the sourdough already will have a considerable impact on the sourdough taste. A sourdough made with salt in it will taste quite different from one without it. I'm not quite sure about why this is, but it may have something to do with the yeasts growing more slowly (more information below).
Both salt and oil will slow down the growth of the yeasts, but don't have much of an effect on the lactic acid bacteria.
Adding oil mainly affects the mechanical properties of the dough (it will be softer and more ductile). It also helps with the structure of the bread (the air bubbles in the bread will be smaller and more uniformly distributed), especially in the presence of an emulsifyer (lard is both fat and an emulsifyer, so it works well in this regard). For this reason, it doesn't make much sense to add it to the sourdough already.
Of course, if the fat isn't tasteless, it will also add to the taste of the bread (I love using natural olive oil in my wheat breads).
Flavor of the bread
Sourdough actually has some pretty complicated chemistry that I know little about. However, here are some effects that I do know:
Lactic acid will give your bread a mild, sour taste. This works very well for wheat breads.
Acetic acid gives you a stronger, more sour taste (very noticable while eating). This works great for rye breads
The amount of yeast in your sourdough also has a big impact on the smell and taste of the bread. Yeast is beneficial to the bread not only for it's leavening properties. Apart from CO2, it also produces ethanol, which will esterify the lactic acid to ethyl lactate over time, which in turn has a strong flavor.
Okay I think that's it. I hope this helps you.
Starters are typically maintained at 100% hydration. That means equal parts water and flour. So, in your case, mix equal parts water and flour. Measure 1 cup of that, and add it to your mix. Of course, this will mean that all of your starter is gone. Alternately, feed your starter (equal parts water and flour) with more than you need, and let it sit on counter over night. Then you you can save the left over to use again next time.
Best Answer
Generally speaking, it doesn't matter that much. The final recipe, technique, and dough composition are all likely have a lot more influence on the final bread result than the composition of your starter (as long as your starter is healthy).
Some people have suggested maintaining different composition starters for different tasks (or to match final dough flour type), but I've never seen any evidence that this produces a significant effect.
I tend to retain whole-grain starters when I am refrigerating them between uses, as whole-grain flour seems to be a slightly more resilient food. (I've had a couple all-white flours go bad in the fridge, but I've never had a whole-grain starter go bad, even after not being used for a couple months. That's just my own anecdotal experience, though.)
If you really want to make sure your starter is ready for a different food in a recipe than it usually has, you can always start feeding it the kind of flour you'll use in the final dough for a few days prior to mixing the final dough. Again, as long as your starter is healthy, it should work fine. Some people claim this has a minor benefit; others say they've never seen a significant difference.