I set up my website and wanted to start with marketing.( getting my name out there)
decided to go with google free listing but they keep suspending my account due to product misrepresentation I have tried just about everything from setting up my policies correctly to removing all my branded products.
I am at my wits end and want to leave the google thing all together.
This is most likely not a Shopify issue but has to do with Intellectual Property law. You stated that Google has suspended your account and you removed the Branded products in an attempt to resolve the issue. Be advised that you need to be authorized to use a brands IP and listing an item for sale without that authorization is illegal. Furthermore if you are dropshipping from a retailer then you are fraudulently misrepresenting the item as brand new when the item is likely materially different and therefore counterfeit.
As far as your marketing goes I would start with your domain then get into PIM, SERP's, and links. Of course this is dependant on your being able to source authentic product and become an authorized reseller.