By deafult, the new drive will take the next available drive letter, maybe D or E or F, depending upon what other drives (e.g. CD, DVD) that you have installed. You can always change the drive letter later.
If existing C is so full you have no room for additional programs, youd' be far better off moving some of the data to the new drive once it is installed. Although you can install programs elsewhere other than C:\Program Files, it makes sense to keep them all together.