Where you register your domain name and where you host your site are separate issues, although the same companies often offer both services and will try to up-sell you from registration to hosting. But you should decide independently.
DNS is normally handled by the hosting provider. But you can do that separately, as well. E.g., in our case, we have multiple locations. Only our main (www) site is at FutureQuest. We have other locations (e.g., you could have an Atlanta office reachable via atlanta.example.com and hosted right on the Atlanta office's main server). This is handy for running VPNs and such between locations. Ask your prospective hosting provider for advice if you such a requirement.
We've been using FutureQuest for the last eight years. We don't have a shopping cart function, but you should be able to set one up there.
Where you register your domain name and where you host your site are separate issues, although the same companies often offer both services and will try to up-sell you from registration to hosting. But you should decide independently. DNS is normally handled by the hosting provider. But you can do that separately, as well. E.g., in our case, we have multiple locations. Only our main (www) site is at FutureQuest. We have other locations (e.g., you could have an Atlanta office reachable via atlanta.example.com and hosted right on the Atlanta office's main server). This is handy for running VPNs and such between locations. Ask your prospective hosting provider for advice if you such a requirement.This is far too much technology for a merchant this size to worry about.
Keep it simple and focus on what you do best.