Getting valid LE certs only requires that the hostname(s) that you’re requesting the cert for resolve to the server requesting them (by default, anyway). You’ll want to make sure you have an A record configured that points to your server. As you’re hosting this at home, you may need to do some port-forwarding to allow this to happen.
As for receiving mail, you’ll want to make sure you have an MX record created that points to your server (unless you are using Amazon SES for mail receiving, which isn’t necessary for maintaining MX reputation).
The setup on Mailcow’s end (in terms of DNS) is pretty much the same regardless of whether you are using SES or not. Take a look at their docs here:
It’s very likely that your residential internet connection is giving you a dynamic IP. If that is the case, then you will need to setup a tunnel or proxy of some kind to ensure that incoming mail can always reach your server. This Reddit thread has some good ideas:
Though I haven’t deployed Mailcow in this specific situation, feel free to message me if I can help at all.