C# standard output

In a C# desktop 2010 application that I need to write, I will be calling a web service. I have been using batch command prompts to save the output to a text file.
  The commands I have been running in the dos window look like the following: cmd1 > file1. Basically the output shows in a dos window and > makes the data displayed in the dos window go to the standard ouput.

My questions are the following:
1. Since I have been using the redirection symbol, the web service must be writing the output to 'standard output' location. However I do not know what the 'standard output' is in a C#  2010 and how to access the 'standard output'. Thus can you tell me what the standard output is and how to access it in a C# 2010 application?
2. Can you tell me how to have information not be displayed in a dos popup window and go to eh location i specify?