What Are the Best Animals for Udhiyah?
Question

What are the best animals for udhiyah – camels, sheep or cows?
Praise be to Allah.The best animals for udhiyah
The best types of animals for udhiyah are: camels, then cows – if sacrificed on behalf of one person; then sheep; then goats; then one-seventh of a camel; then one-seventh of a cow. The best types of animals are those which are fat and have more meat, and are physically complete and good looking. 
In Sahih al-Bukhari it is narrated from Anas ibn Malik (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) used to sacrifice two horned rams that were white speckled with black. 
Abu Sa’id al-Khudri (may Allah be pleased with him) said: The Prophet (peace and blessings of Allah be upon him) sacrificed a whole (i.e., not castrated), horned male sheep, with a black face and black (circles) round the eyes, and black legs. This was narrated by the four. Al-Tirmidhi said, it is hasan sahih; it was also classed as sahih by al-Albani in Sahih Abi Dawud, 2796. 
Abu Rafi’, the freed slave of the Prophet (peace and blessings of Allah be upon him), said: When the Prophet (peace and blessings of Allah be upon him) offered a sacrifice, he would buy two fat rams. According to one version, castrated rams. (Narrated by Ahmad, classed as sahih by al-Albani in Sahih Ibn Majah, 3122)
Fat means an animal that has a lot of fat and meat. Castrated means one that has had its testicles removed – this is usually better than an uncastrated animal with regard to the taste of the meat, but the uncastrated animal is more complete in a physical sense. 
These are the best kinds of sacrifice with regard to type and characteristics. 
What animals should be avoided in udhiyah? 
With regard to those that are makruh to slaughter for sacrifice , they are as follows: 

Those who have had one half or more of their ears or horns cut off.
Those whose ears have been slit crosswise from the front.
Those whose ears have been slit crosswise from the back.
Those whose ears have been slit lengthwise.
Those whose ears have had a hole made in them.
Those whose ears have been cut until the ear channel is visible; or it was said that the same [Arabic] word means those that are so emaciated that there is no marrow in their bones.
Those whose horns have been removed entirely.
Those that are completely blind even though the eyes are still present.
Those which do not follow the flock and join it unless they are herded and driven to do so.

These are the animals that it is makruh to sacrifice, as narrated in the hadiths which forbid sacrificing those that have these faults or enjoin avoiding such animals. This is understood as meaning that it is makruh, when these reports are taken in conjunction with the hadith of al-Bara ibn ‘Azib (may Allah be pleased with him) who said: The Prophet (peace and blessings of Allah be upon him) was asked, “What should be avoided in the sacrificial animals ?” He gestured with his hand and said, “Four: a lame animal which is obviously lame, a one-eyed animal whose defect is obvious, a sick animal whose sickness is obvious, and an emaciated animal that no one would choose.” (Narrated by Malik in al-Muwatta) 
Animals with similar faults are also added to this list, so it is makruh to sacrifice the following kinds of animals: 

Camels, cattle and goats that have had half or more of their tails cut off.
Those which have had less than half of their fat tails cut off. If half or more has been cut off, then according to the majority of scholars it is unsuitable for sacrifice. If it was born that way, however, there is nothing wrong with it.
An animal whose penis has been cut off.
An animal that has lost some of its teeth, whether incisors or molars. But if it was born like that it is not makruh to sacrifice it.
An animal whose teats have been cut off. But if it was born like that it is not makruh to sacrifice it. If its milk has stopped flowing but its teats are intact, there is nothing wrong with it.

 If these five are added to the nine mentioned above, the number of makruh animals reaches fourteen.
For more, please see these answers: 192041 , 126705 , and 106597 .
And Allah knows best.