DNS services cost money, either in staffing or recurring charges, so it really depends on your budget. Neustar is a nice DNS provider ($50+/mo).
Generally you'll want to set up your new DNS, turn down the refresh on your existing DNS domains, wait $old_refresh or so, then change your primary/secondaries listed at your registrar to point at your new DNS.
I have to disagree with your 'Neustar is a nice DNS provider' statement. I used them for 2 years, most of that time I was unhappy but because I was locked into a contract I had to wait it out or else pay a hefty breakage fee.
Their website/UI wasn't any good, very dated, they even rolled out a new one before I left, but that was horrible, they used AJAX everywhere, just for the sake of using it, and it made usability horrible.
Their support sucked as well, you would need to submit a ticket, and they take forever to get back to you, and they don't say anything besides "it looks fine to me". If you try and call them, you end up talking with someone who has no idea what they are talking about (same customer support line, for multiple products), or they don't speak english well.
You end up paying per DNS query, which is a really expensive way to pay for DNS, we were paying thousands of dollars a month to them for DNS alone.
Their advanced DNS services (DNS load balanceer and DNS failover) where very basic, and getting them setup correctly was a PITA.
There DNS service was nice until it crashed, which didn't happen often, but when it did, it took down half the internet with them.
I personally wouldn't have picked them to be our provider if it wasn't for one of our investors telling us how great they are and we needed to use them. I should have listened to my gut, but I also didn't want to piss off the guy paying the bills.
YMMV, but I would say, stand clear, and go to one of the newer folks doing the same thing for much less the cost, and more features.
This recommendation suprises me. Do you have particular reason to recommend them? $50 per month for DNS strikes me as ludicrous, but I suppose it's worth it for some sites if they truly can provide a more reliable service.
But I don't find the quotes on their website to be confidence inspiring: "UltraDNS manages and maintains its own industry leading resolver platform; as a non-open source platform it isn't prone to hijacking, spoofing or viruses".
And their industry positioning scares me:
The revised bill would place a ".kids" subdomain under the
control of NeuStar Inc., the Washington-based
telecommunications company that won the contract to manage
the ".us" country-code domain last fall.
NeuStar would be expected to police the subdomain to ensure
it remains free of inappropriate content, and it would
answer to the Commerce Department's National
Telecommunications and Information Administration.
Web sites in the domain would be prohibited from linking to
sites outside it, and they could not set up chat rooms,
instant messaging or other interactive services unless they
could certify that they did not expose children to
pedophiles or pose other risks.
If privately held NeuStar were to lose money on the
venture, it could give control back to the Commerce
Department, which would seek another operator.
ps. You're probably aware, but I was checking if the site listed in your profile was served by them, and noticed that many9s.com looks to have expired over the weekend.
Generally you'll want to set up your new DNS, turn down the refresh on your existing DNS domains, wait $old_refresh or so, then change your primary/secondaries listed at your registrar to point at your new DNS.