If your supplier provides a spreadsheet for shipping rate, we can help you setup the rates on your store using our app, JsRates. JsRates has free demo plan; install it and reach out to our support team for free setup service.
To sync inventory from a database, you might find Stock Sync app handy: https://apps.shopify.com/stock-sync
To upload products to your store, Matrixify app might be useful: https://apps.shopify.com/excel-export-import