The address does not matter. I have been using the Remote Administration on various D-link routers for year from different public IP addresses. Some matched but most did not.
As for the private IP addresses, the established private IP addresses ranges should be used. If you happen to use a public IP range, as a private one, you can have web access problems.
Established Private IP address range
Class A 10.0.0.0 – 10.255.255.255 = 16,777,216 "addresses"
Class B 172.16.0.0 – 172.31.255.255 = 1,048,576 "addresses"
Class C 192.168.0.0 – 192.168.255.255 = 65,536 "addresses"