Hi,
I think you need to think about link building as "why would people want to link to my site?".
The problem with e-commerce is that quite often the products you sell will be no different to the products on other sites and therefore there is no USP or Unique Linking Proposition, in this instance.
The most controllable way of building links is to plan a content strategy.
- Think about where you want links from (which sites)
- Research what type of content they link to
- Create content that they are likely to link to
- And contact them to make them aware of the content you've created
The last point works even better if you get them involved in the content creation purpose. There is loads of advice on various content marketing and link building strategies over in the blog.
Your idea about getting links from manufacturers isn't a bad idea but it isn't scalable.
The important thing to remember is that if you approach this with a short term "get as many links as I can" point of view, you'll be wasting your time. If you approach this knowing that it is long term and will take time and effort you'll be on to a winner.
I hope this helps!