In the book Twilight the family members do not drink human blood unless they have an accident and have to eat it. They tend to search out animals for their blood. This leads to different family members having preferred types of blood. Emmet has a favorite penchant for the blood of a Grizzly Bear. Edward likes the refreshing taste of the blood of a mountain lion. It turns out that the family members are drawn to drinking the blood of large game animals and find the most satisfaction from their blood.
It never states every family member's favorite animal to feed from. However Bella asked about something along the line once and he told her that Emmett's favorite animal was a grizzly bear, which from his near death experience when he was human was understandable. Then Edward said he preferred mountain lions.
In the twilight series, the characters don't really have a favourite animal to drink the blood from. However, in the book Emmett is said to prefer a grizzily bear but this is because he enjoys the fight he has with them, not because it tastes better. Edward also says that he likes a mountain lion, his family compare him to a mountain lion when he hunts.