Gamepress has an entire article about the best pokemon for Ultra. Spoilers: It's Giratina. Kingdra, Blastoise I hear are amazing as well.
For Great, the obvious trio many people are now familiar with is Azumarill, Altaria, Cresselia. Some other good ones that spring to mind immediately are Whiscash, Meganium, Lanturn, Kingdra, A-Muk, Forretress, Umbreon, Flygon, Skarmory. I don't have a set team but if I want to make a strong team, it'll almost always include at least one from the big three due to their sheer power.