Verizon Static Unrestricted

[JustusIV]

I am seeking advice. Turns out through my work Verizon will give me a Static Unrestricted IP (Do i need one. No. Do i want to play with one. Yes. Why. Fun). What are some of the security implications of this? I have done some of my own checking with some tools like shields up and see 3 ports that are rejected as opposed to timing out. So people know something exists on the other end and could maybe even determine the OS based on that.
Any additional info on this subject would be amazing.

Thanks