The best animals to be sacrificed are camels, then cows, then sheep, then to share in a sacrifice
Question

What is best for the sacrifice – to slaughter a sheep or to have a share in a cow?.
Praise be to Allah.The best sacrifice is a camel, then a cow, then a sheep, then to have a share in a cow. This is the view of Abu Haneefah and al-Shaafa’i, because the Prophet (peace and blessings of Allaah be upon him) said concerning Jumu’ah: “Whoever comes at the earliest hour, it is as if he sacrificed a camel. Whoever comes in the second hour, it is as if he sacrificed a cow. Whoever comes in the third hour, it is as if he sacrificed a horned ram. Whoever comes in the fourth hour, it is as if he sacrificed a chicken. Whoever comes in the fifth hour, it is as if he sacrificed an egg.” Narrated by al-Bukhaari, 881; Muslim, 850. 
It is a sacrifice by means of which one draws closer to Allaah, so the best (to be offered) is a camel, as in the case of the hadiy (sacrifice offered by the pilgrim on Hajj). 
A sheep is better than sharing in a camel, because the aim of the sacrifice is to shed blood. A ram is better than a sheep (ewe), because that is what the Prophet (peace and blessings of Allaah be upon him) sacrificed and the meat is better. End quote from al-Mughni, 13/366 
The Standing Committee was asked: Which is better for sacrifice, a ram or a cow? 
They replied: 
The best sacrifice is a camel, then a cow, then a sheep, then a share of a camel or cow, because the Prophet (peace and blessings of Allaah be upon him) said concerning Jumu’ah: “Whoever comes at the earliest hour, it is as if he sacrificed a camel…” 
The point here is that there is an order of preference between camels, cows and sheep in drawing close to Allaah through the sacrifice. Undoubtedly sacrifice is one of the greatest acts of worship through which we may draw closer to Allaah. A camel is more valuable and more useful. This is the view of the three imams – Abu Haneefah, al-Shaafa’i and Ahmad. Maalik said: The best is a young sheep, then a cow, then a camel, because the Prophet (peace and blessings of Allaah be upon him) sacrificed two rams, and he (peace and blessings of Allaah be upon him) did not do anything but that which was best. 
The response to that is that the Prophet (peace and blessings of Allaah be upon him) sometimes chose the option that was not the best option out of kindness to his ummah, because they follow his example. He (peace and blessings of Allaah be upon him) did not want to make things difficult for them. He stated that the best is a camel, then a cow, then a sheep, as stated above. And Allaah knows best. End quote. Fataawa al-Lajnah al-Daa’imah, 11/398. 
Shaykh Ibn ‘Uthaymeen said in Ahkaam al-Udhiyah: 
The best sacrifice is a camel, then a cow, if one offers the whole animal, then a sheep, then a goat, then one-seventh of a camel, then one-seventh of a cow. End quote.