If you want to achieve 'total search dominance' for blankets you're up against a lot of big retailers (search for 'blankets' and you'll see some of the sites you're competing with). You'd need to think 'big brand' for your site, so it has to look great, be full of compelling content that searchers are looking for, and have a wide range of products that meet their needs across ALL of the search terms you want to dominate (as
@fisicx says a limited range won't help you if people are seeing stuff they don't like and bouncing back go Google - you'll actually move down in rankings). Oh and lots of links to that content of course too (not rubbish easy-to-get ones either, natural, quality links).
Assuming you don't want to hire and agency and you want to do everything in house here are the things you need:
Web designer - make the site look 'best in class' and then work on the linkbuilding content with your writers
Conversion expert/UX expert - later on once you have traffic you'll need to be testing endlessly to improve sales and conversions - big ecommerce stores do tons of this... you'll at least want to dip your toe in and make sure there aren't any obvious (to an expert) leaks in your user flow
Content writer - for sales page, product copy, blog, linkbait type content (things that are designed to be easier to link to than an individual product listing but still super relevant to your business). You'll need a lot of content.
Outreach expert - for getting those links, promoting your content, getting press coverage and all those kinds of things.
As others have noted there might be easier places to start such as social advertising (Facebook ROI is often really strong for ecommerce stores), PPC (for sales and for helping you define which keywords are most profitable for your future SEO efforts), etc.