Ecommerce or something else needed?

I recently purchased a company and am having problems with the website, specifically lack of traffic and visibility. I was told that it use to be an e-commerce website but was recently changed to more of a blogging style. One of our biggest problems is we have to update it constantly with new products as we sell live animals and update each one’s profile as they come and go. Therefore, I have been researching ecommerce plugins. However, I do not want to have any kind of sales or checkout process on the website. Just a specific list of the dogs and a general list of other products. A large problem with what we have now is that we are getting poor SEO scores on almost all of our pages. Any help and/or recommendations would be greatly appreciated.