Welcome Vamaz.
There are many things that you need to look at to determine what size pipe you need. You need to know how big the watershed is and what kinds of soil you have. A watershed with a lot of sand will have less runoff than one with all clay soils. You need to determine how much runoff you will get from a certain amount of rain. If you have a small watershed a 6" pipe would probably work well. If you have a large watershed even a 12" pipe may not be big enough.
This link will help you figure out how big the watershed is.
http://acme.com/planimeter/To find out what kind of soils you have do a search for web soil survey on google.
