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For the site speed, Thomas gave a lot of great tips in his comment above. For backlinks, I would recommend starting with a competitor backlink analysis using Moz's Open Site Explorer, Ahrefs, or SEMrush. Simply put the websites you see ranking high on page 1 of Google for the keyword phrase you would like to target and see what "dofollow" links they have going to their website. Once you compile a list of the backlinks your competitors have see which ones you can go after. The best way to get backlinks is creating awesome, shareable content that is helpful in your industry, and then promoting it and doing outreach for it in any way possible. This can be in the form of a blog post, guide, or resource page on your website. Some quick backlink wins though, would be doing a press release and getting listed on high DA directories (see Moz local).