Iptables: dropping/rejecting new and invalid connections

Question

I'm very new to iptables and my goal is the block NEW and INVALID connections on the INCOMING chain and log any attempts for a NEW connection.

I'm also letting any and all traffic out on the OUTGOING chain.

This is what I did:

sudo iptables -A INPUT -m conntrack --ctstate ESTABLISHED,RELATED -j ACCEPT
sudo iptables -A INPUT -m conntrack --ctstate NEW,INVALID -j LOG
sudo iptables -A INPUT -m conntrack --ctstate NEW,INVALID -j DROP

When I add the last line I can no longer get out on the web.

My current setup is an old Macbook Air bridged with a VirtualBox VM running Ubuntu 14.04 LTS. The Air will eventually serve as my firewall between my router connecting to the Internet and my internal network once I get the iptables working correctly.