1. About rankings: usually, one can avoid/minimize rankings decrease by implementing "301 Moved Permanently" on the whole website or for every page of that. Since Zoovy is a hosted cart, that probably will not be possible -- but you should check.
Optionally, you can move your entire domain to your new OsCommerce hosting, and create products/listings pages there that would imitate old pages you had on Zoovy. then redirect each of this page to your new corresponding OsCommerce product/listings page.
On Apache, you can achieve that with .htaccess files.
2. OsCommerce is not exactly a pot of honey. It's crappy, and it's hard to customize. The only value I see is that it's free, and has a lot of add-ons. If you leave that with its default awful design, that will scare away 90% of your potential customers.
Surely, you can start with that if you're a programmer, otherwise you have to hire a PHP programmer. Might cost more than you pay for Zoovy, with unpredictable results.
My suggestion would be to start an alternative OsCommerce store (if you decide) before moving away from Zoovy, then if you're satisfied with that, move your Zoovy domain to your new hosting and implement redirect for every product/listing/content page you have.
That won't guarantee you avoid rangings drop, but should minimize that.
Hope that helps!