With WordPress you would definitely be able to start quicker. Joomla has a slightly steeper learning curve but it gives you a lot more control when it comes to customization. WordPress would be my recommendation for total non-techies who mostly care about putting the content online but I would recommend Joomla for people who are looking for more control of their site.
Joomla isn't that bad comparing to other CMSs out there. It takes a little to get used to it but then it becomes very intuitive.
Both WordPress and Joomla will run fine on GoDaddy. Where you may run into problems with GoDaddy is when you are ready to integrate with a payment gateway to charge credit cards but sounds like you are not at that point yet.