I ran iptables -P INPUT DROP to block all incoming packets.
Then I allowed packets belonging to related or already established connections to be allowed with iptables -A INPUT --match conntrack --ctstate RELATED,ESTABLISHED --jump ACCEPT
Opening the browser and navigating around made me realize that DNS was not working. Only after sudo iptables -A INPUT -p udp --dport 53 -j ACCEPT it worked.
So I wonder: "Why do I have to allow the destination port to be reachable on input? I'm connecting outwards to a DNS and the answer should be to a highport".