How to "legitimize" the relationship with the client LLC?

Question

Individual entrepreneur

Hello.
In order to continue cooperation with the customer for the development of the site, he wants to draw up an employment contract with me as an individual, or I can register as an individual entrepreneur (he is an LLC)
.
I did not find a completed example of a contract in the jar.
I can’t understand:
- I sign an agreement with him as a physicist, then below in the details will be my address of permanent registration. Correctly?
- if I make an individual entrepreneur, then in the details, in addition to the Unified State Register of Legal Entities, will there be my address of permanent registration or can I put a temporary one? (I do not live at the place of registration). And you will have to go to another city to issue an IP.
Thank you.