Should I offer free shipping above a given price and just include the cost in my product prices on Shopify?

If you are Dropshipping, then you should just add the shipping cost to the total and give free shipping. People generally don't seem to mind waiting a few more days if they don't have to pay for shipping.

I would advise against marking up your product price to offset shipping. Price is the first thing people see and this tends to turn away sales, whereas if your product price is lower and shipping is added after, people will be more willing to purchase your products.