You will definitely want to host it somewhere else, what happens when your power goes out? Cable internet goes out? Oops, website no longer online
I've spent thousands and thousands of dollars on hardware to protect all my customers including firewalls, intrusion prevention systems, etc etc.
There is a lot that goes into hosting a website that most people do not understand, and that's why you need to find a managed host. They will provide you support whenever you have problems, and will handle making sure you website is online 99-100% of the time, even protecting your site from malicious users who could try and hack into it and obtain all your customer information. There's a lot that goes into security and you will just need to ask yourself whether or not it's worth the $5 a month to let someone else handle it...that's how much you probably waste in one day at McDonalds.
What kind of store are you trying to start? There's a lot of scripts that can do this but you probably need to make sure there isn't something already out there specifically for what you're trying to do.