You absolutely can get your drink to go. We took our drinks all over Epcot, no problems.
As for favorite drinks? They're all delicious!
If you're more of a sweet fan, the avocado (I know, it sounds odd..) is delightful. It's a frozen drink, but it's delicious. The cucumber is similar, but not frozen, it's served on the rocks. Also delicious.
If you're feeling adventurous, go for the Jalapeno. It's got a bite, that's for sure, but it's awesome. The tender made ours with fresh crushed jalapenos, and I loved it.