Website Transfer, Tidy Up and Update

We have a basic website and need to transfer it away from WordPress (GoDaddy) to something more manageable and flexible. Happy to continue hosting through GoDaddy if needs be, however we want a neater and less restrictive web design that WordPress just cannot offer us.We want to keep the domain name and 3 email addresses attached to it. We have some new content to add, but are reluctant to do so until we have a better site as using WordPress will just start making it look messy.