First day on the internet? o_O
There are a billion random bots poking at random IP's random ports at random times. 99.99% of these won't ever get past your router's firewall. It's really not something to worry about. If anything, you should look out for unusual outgoing traffic.
If you want to protect yourself from the absolute worst case scenario, disconnect. The only way an external party can do anything is if you have an external connection. That's why there are certain computers in certain missile silos that have never been or will ever be online.
Realistically, though, you really aren't special enough to be hack-worthy (no offense), unless you work for a bank, or the government, or something like that. Even then, it would be your work networks that would likely be targeted, and they'd have paid staff just for NetSec.
Don't lose sleep over it.
-McD