Digital Ocean doesn't provide a service like the one you're looking for -- but there is a way to use NameCheap's services and still have your name point to your droplet.
The consequence of using NameCheap's name servers instead of your own is that things like PTR records will be handled at NameCheap, not here on Digital Ocean. But ths is probably what you want. Also, f your IP address for your droplet changes for any reason, you'll need to go to NameCheap to update it. The same is true for adding subdomains, etc.
You should now be able to forward mail using NameCheap, and access to your host name should point to the droplet.
EDIT: Any idea how to do second-level indentation?
EDIT 2: Oh, the markdown's not working properly. ..anyways, the last two list items above should be indented.
EDIT 3: Also, note that the service provided by NameCheap is only a forwarding service, you won't be able to set it up in gmail as a proper email address.
+1 for postfix. Here are a couple more excellent tutorials on the subject:
I just tried the NameCheap experiment on one of my domains. Handed control of DNS back to them, set up a forwarder, gave it a while, and sent a test that successfully forwarded to GMail. There's one downside though: GMail displays the incoming message as coming from:
John Doe via registrar-servers.com
That "via" part is not a very professional appearance - kind of weird and off-putting for recipients. I think I'll go for the postfix setup after all.