For any shopping cart service, you will have to buy a domain name, have it hosted at a hosting company compatible to your shopping cart. You can also have wordpress installed on the domain – but you don’t really need to.

Looking at the intuit.com site, they say hosting packages with large companies such as homestead, godaddy, ultracart are all compatible with their payment method. So what you do is get a hosting package with either the Fantastico (Cpanel product) or other MySQL database – install Wordpress on the database – hook it up to the shopping cart (make sure you get a SSL), then connect it to your merchant services. Sounds complicated, but not really.
References :
Worked for a web hosting company awhile back – in tech support. Now I work for others like http://powersellermentoring.com and http://cryptidresearch.com