Public IP address

I'm getting ready to switch ISP to one that has unlimited, so I don't have to worry about going over the allotment. The packages for 10 & 15 meg down have a public IP address.

I'm not sure I want a public IP address. How does that affect security?

I don't plan to run a server.

Will hackers be looking for public IP addresses to hack?

Should I get a better router with better security features? I have a Tplink ac/b/g/n.

I'm going to keep using the Netgear hotspot for when I'm away from home.