Thank you for posting your question. Apologies for the delayed response.
I would recommend checking out the apps for Shopify listed on our website (see link below) and take a look at those with higher star ratings and the most reviews. Then read the comments on those reviews to get a better idea of the what the product experience is like.
what I understand is that you need to post the Orders from Shopify to QuickBooks and also sync the inventory between QuickBooks and Shopify. For that, there are multiple apps available. You can try Webgility Desktop which not only connects to QuickBooks all the versions and Shopify but it will also sync Inventory from QB to Store or Store to QB. There are other Apps available in the market like T-hub or entriwise . You can check them too.