Whatever you do, make sure not to trust data sent from the client. $_SERVER['REMOTE_ADDR'] contains the real IP address of the connecting party. That is the most reliable value you can find.
However, they can be behind a proxy server in which case the proxy may have set the $_SERVER['HTTP_X_FORWARDED_FOR'], but this value is easily spoofed. For example, it can be set by someone without a proxy, or the IP can be an internal IP from the LAN behind the proxy.
This means that if you are going to save the $_SERVER['HTTP_X_FORWARDED_FOR'], make sure you also save the $_SERVER['REMOTE_ADDR'] value. E.g. by saving both values in different fields in your database.
If you are going to save the IP to a database as a string, make sure you have space for at least 45 characters. IPv6 is here to stay and those addresses are larger than the older IPv4 addresses.
(Note that IPv6 usually uses 39 characters at most but there is also a special IPv6 notation for IPv4 addresses which in its full form can be up to 45 characters. So if you know what you are doing you can use 39 characters, but if you just want to set and forget it, use 45).