@kamstan6

If you plan on using DigitalOcean for your DNS, you'd simply setup your domain through the control panel (under Networking) and then modify your DNS zone accordingly.

For example:

A          @          DROPLET_IP
A          mail       HOSTGATOR_IP
CNAME      www        yourdomain.ext
CNAME      mail       mail.yourdomain.ext

MX         @          mail.yourdomain.ext          0

DROPLET_IP = The Public IPv4 IP of the Droplet you deploy.

HOSTGATOR_IP = The IPv4 IP of the web server your account resides on.

yourdomain.ext = Your actual domain name + extension.

The only thing you'd need to keep a look out for is when/if HostGator changes their IP. I've ran in to this a few times on setups with clients I've worked with in the past across a number of providers, so in the event they change the IP, you'll need to change the IP listed in your DNS to match. It shouldn't happen often, but moving accounts around is pretty normal, so it's possible for it to happen a few times.