I am adding a bathroom in my house and plan on running a new circuit to service the room. I purchased a GFI outlet as I believe this is required by code. To protect the entire circuit, does the GFI outlet need to be the 1st receptacle in the circuit or does it protect the entire circuit regardless of placement?

IF you want to protect the whole circuit it must be first in line and wired properly to LINE and LOAD.

There is no reason to protect the lights though. Was there a reason you want to have the lights GFI protected?

To clarify, line side will be the power coming in, load side will be power out to the devices you want to protect.