Google doesn't recognize a site any differently based on template. Their algorithm includes over 200 different aspects of a site (according to Google), but template is not one of them. Use whatever template and whatever software you like, and confidently know that you are safe with it as far as Google is concerned. I would use a mixture of a free shopping cart software like x-cart or 3dcart, and PayPal (which has a lot of extensive options if you have a cheap merchant account) and Google Checkout (which also has a lot of extensive options). Ask any more questions if you have them.
However, you addressed Google, so I'll give you some Google tips as well. Here are the best ways to be noticed, indexed, and ranked high with Google:
-Links: Your PageRank is important. Get links out there everywhere you can, but be selective if you have to exchange links. Don't go to home improvement corporations and florists. If you have a lot of link exchanges all willy nilly, they will blacklist you, so do it with quality links only. If you are putting links on forums, blogs, and other places that YOU can put them, go for it. Go on a link binge.
-Register with Google, Yahoo, and MSN.
-Register with Yahoo Directory and DMOZ. (DMOZ is Google's directory service.)
-SEO (Search Engine Optimization): Use words and phrases throughout your site in such a way that they reflect the search phrases you want to optimize for. That includes your title, descriptions, and captions. Create a caption for every image you have, and even put an image description in your image source code.
Creativity Unlimited, my full time business, is a company that specializes in
creative services, including web design and search engine optimization. For much more information, or to ask any questions, feel free to contact me through my website. (Click the link I added at the beginning of this paragraph.)