type of visa required if I want to stay with my friend

You can apply for Tourist L type for visiting China and your friend.
For applying a Tourist L, you can ask your friend to write you an invitation letter. Then you can use the letter, your valid passport, application form, recent taken photo, your personal statement, your work proof or bank statement to apply through the nearby CVASC.

For extension it, you need to prepare your valid passport, an application form with recent taken photo, your Temporary Accommodation Registration Form issued by local PSB, your friend's residence permit. Then you can go to the local Exit-Entry Adminstration Bureau for applying.