I don't grill....how would I get this done in the oven?

Watch where you buy your shrimp. If you do not have access to fresh wild-caught shrimp, check the country of origin. Many times farm-raised shrimp are bathed/soaked in a preservative solution that also may mask any odor. Keep in mind you may be better off buying still frozen shrimp as shrimp on ice in the seafood case are typically thawed at the store and you won't know how long they have been sitting there.

Either sear them in a roaring hot cast iron skillet, or broil them with the oven rack placed in the highest position, same timing as you would grill them. Be sure to choose larger shrimp, which are meaty enough to withstand the intense heat for that timing and still end up juicy. Hope you'll love the recipe ;)

A grill pan is a good option.

I would not use the oven, it will dry them out. Sauté them on stove top.
If you are not used to cooking seafood, try doing a couple of shrimp and tasting them before you sauté them all. That way you will see how fast they cook and if you need to adjust the heat, etc…