Migrating email and web-hosting from single provider to separate providers?

We've had our website and email with a single provider for a long time but they are now price gouging so we are planning to move to new providers. Looking at our options, it looks like MS Outlook for email and Wordpress for the website are our best options. Our domain is registered through GoDaddy. Any weirdness come up with having the DNS for email point to a different provider than the website?