Smarthost likely required
A lot of large ISPs block any inbound mail from subnets that are believed to be 'end user' IP addresses and thus not expected to be delivering mail - see https://www.spamhaus.org/pbl/ for an example - as such if you do host a mailserver yourself you would be well advised to use e.g. your ISPs mail server (if it will accept mail for non hosted domains) as a smarthost for outbound mail otherwise you'll find quite a few destinations rejecting it.
Also re: dynamic IPs - there is a big risk in using a DDNS service that if your connection goes down, you won't update the DDNS name until it comes back, at which point you might find people delivering mail to someone entirely different who happens to have got your old IP - while in most cases that person won't be running a mailserver, if they are then they can either steal your mail, or if they reject it as an invalid recipient the other end will bounce it back to the sender, which I suspect is not what you want...
Biting the hand that feeds IT
