The question 'Securing small home automation setup' provides a useful reference for general security tips, but there are also some specific steps you should follow to keep your Raspberry Pi secure.
Steve Robillard's answer to a question on Raspberry Pi Stack Exchange outlines some of the specific issues with using a Pi that you can address, such as changing default passwords, using
iptables, etc. He also helpfully links to the Securing Debian Manual, which, although very large, is incredibly comprehensive, and covers most major concerns.
Since you'll likely be connecting to the Pi through SSH, consider key-based authentication instead of using a password—a SSH certificate is virtually impossible to guess, even by a determined attacker, unlike a potentially weak password. As noted in the linked article, also take a look at Fail2ban, which will IP block any users who show malicious signs (e.g. incorrect password guesses).
Regarding your DDoS concerns: if someone decides to launch a DDoS attack against your Pi, you stand very little chance. Some attacks can reach up to 665 Gbps, which would be impossible for your Pi to defend against. But, I would pose this question: why would an attacker want to DDoS your Pi? Denying you service would probably not provide much benefit to an attacker, and a lot of IoT devices are instead being hacked to participate in DDoS attacks.
Nevertheless, if you were very paranoid, you could perhaps whitelist devices that your Pi was expected to connect to, and simply drop any other packets with
iptables. It's up to you to decide if it's worth the trouble.
Regarding DDNS, I find HowToGeek's guide quite clear—essentially, you need to check your router for a DDNS setting, and configure that. NoIP have screenshots for most major router models. You'd probably have better luck asking this separately (and you may already find an answer on Super User).