Transfering your store for $19 doesn’t mean that your rankings won’t suffer. Most likely they will no matter what you do. The question is how badly do you want to suffer?
Ideally, every page URL will be 100% the same. Start there. If you can’t make every single page URL the same you will need to put in 301 redirects for every page that is different and point to the new page.
But even if the rest is the same – the content, prices, meta tags site structure, your site will still be impacted because Google will devalue it as it indexes the new site.
The duration of that will depend on many things including the amount of change, how often your site normally changes, the number of links you have and so on. Really too many factors to mention.
but long story short, your site will lose rankings – at least short term – and some may never recover, but you will also gain some you’ve never had. You just have to wait it out.