Eye of round is the traditional roast beef you find in the deli cases. Easy to spot by it's translucent rainbow. Yes, it tends to be dry due to practically no marbling.
I think rib roasts are the best for roasting. If you buy a boneless one, they don't take nearly as long to cook. Reverse sear is the way to go for wall-to-wall pink. Best on a grill with good temperature control (like a kamado), but you could improvise with your oven and a screaming hot cast iron skillet (and an open window) at the end.
FWIW, my favorite 'roast' is actually a braise. This recipe is fool-proof:
https://www.cookinglight.com/recipes...beef-pot-roast