If you plan to apply citizenship in the future, you also need to apply N-470 beside the I-131. I-131 takes about 9 months processing.
you can check the current processing time for I-131 (reentry permit) on USCIS website.

It is a very straightforward process. Basically, you do not need the proof of anything. An application form is fine. Go to INS(home land security) website and down load the form by yourself. I never used a lawyer.
One trick is you MUST apply for it when you are physically in the states.
Now if you are planning to work in China, and intended to keep your greencard status AND wants to become a citizen someday in the future, you also need to apply the status to keep the continuity of your residence. If you come back every six months to the US, continuity application is not necessary. ..

showing the receipt. Didn't have any problem. Receipt is good enough.

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