The answer is "it depends." What are you trying to accomplish, exactly? If you are just setting up a web site, your ISP is probably a better option for hosting the zone files for your domain.
Unless you plan on having a lot of servers and/or you WANT to have control over your master zone file, it's safer to leave it to the experts, because if you screw something up your site and/or email capabilities could go down. Your ISP is going to bill you for the time spent troubleshooting issues which you are responsible, and fatfingering a zone file is your responsibility.