Hank here from Shopify.
Currently, this is the list of the supported Payment Gateways in the U.A.E.
With regards to which payment provider works well, all of the above integrate perfectly with the Shopify platform but 2Checkout and PayPal Express Checkout are two very popular forms of gateways. 2Checkout would enable you to offer card payments like Visa, Mastercard, Amex, etc. While PayPal Express will allow your customers the option to checkout using their PayPal account.
I find having those two payment gateways active gives you a wide coverage of ways to offer your products to be purchased by your customers.
Let me know if you have any further questions about this, or which payment provider you went with for your store!
All the best, Hank.