I've got limited experience with web domain registering/hosting, and none with e-commerce. 

my reference is ryanbrosinc.com - our family website you can use to clearly see how limited my experience and capabilities are.

You will need to have a domain registered - if not familiar this is the address people can find it at. This is around $15/year and SEVERAL companies are available for this service...but I'd just get it included with your hosting service provider. Hosting is probably what your are researching - who will have the template and forms you can build from and where will the digital files be managed/stored for 24 hr access. Our web is hosted by Bluehost, and they have web domain registering and email client too. I believe they can tie in e-commerce but you have another level of management on your end to setting up that catalog, updating pricing, inventory, photos, etc... so we have not gone that route. 

Any e-commerce plug-in (if you can call it that) will have a fee for processing payments, which is most likely in addition to the service fee the credit card companies charge. 

Barn2Door.com is maybe a better option for you if all you are selling is your family meat. They handle the Search Engine Optimization to get your business/farm/family to pop up for anyone in Riley County looking for farm-to-fork meat in Google. We looked into them briefly, I'm not endorsing them and have no actual experience other than their awareness.

Best of luck, let us know when you're online.