Rebranding, new domain, same products

Hi,

We're re-branding over the next month or so, everything stays the same product wise, it's just our current brand name / identity pigeon holes us, so a new look and name is in order, and therefore a new domain.

I've been tasked with helping out with the SEO side of things, but it's all new to me having only really worked in PPC previously, i understand bits and bobs but nothing more.

Having spent the past couple of days looking into it, as you're all well aware there is a hell of a lot to digest, from 301 redirects to external linking tools etc... but what I would like to know is what should be my main focus(es), given I'm not 100% sure what takes priority?

FYIs - we currently rank very well organically, only Amazon and eBay really rank above us, if ever, and they always should link to our products as we more or less have a monopoly on a lot of what we sell (although there are sellers / sites selling unlicensed products).

Thank you in advance.