Hi Karine,
Here are a few ideas, obviously this is early days so there is a lot more than this to do.
Looking at the site I would say for your two main category pages you need more rich text content relevant to the product category. Using images like the homepage rotating images is fine but try to have the text parts as CSS text rather than images so that Google can read it, or at least a good descriptive alt text per image in this section.
Your page titles are too long, focus on the main product keyword, this should be fairly straight-forward, do product type - product name - sitebrand, keep them below 70 characters.
The site at the moment doesn't have a lot of products, but no doubt you will build that up. However, it is a competitive area, so rather than just going for less-competitive keywords using a keyword tool that everybody uses, think about your offering and why someone should visit your site rather than go elsewhere.
You really need to have in mind what your unique selling points are and who your target audience is, then create titles and content that are relevant. Segment your offering and target specific customer types and you'll naturally find less competitive (& long-tail) potential search terms.
Yes you need to continue link-building, but do read up on the various guides and posts here about what makes a good inbound link - Quality over quantity every time.
As a new site using PPC is not a bad route to drive initial traffic, you can set limits on how much you want to spend and your type of visitor will hopefully be loyal because of your great products and service and return again and again. However, once again be aware this is a competitive area so choose your keywords for your campaign carefully. Once again this is when knowing your market and audience helps you target the right keywords.
The point is coming into a mature market like organic care products is never going to be a quick success, you need to think about getting the word out through any channel you can, good luck.
