I can highly recommend keeping your DNS stuff separate from hosting. For 'critical' stuff I've been quite happy to use DNSimple for that, and regular mom-and-pop LAMP hosting for the actual site.

In some cases I pipe it through Digital Ocean, because it's nice to have everything in one place, but I've wondered if that might have some performance impact. Can anyone confirm/deny this? So, domain registrar -> Digital Ocean -> hosting.

Your edit is right panel.dreamhost.com doesnt resolve. But when it loads it does have the ability to specify nameservers.