Some scholars say that *Wearing any ring is not Sunnah since the Prophet Mohammed (PBUH) used to wear a ring for signing letters sent to other kings. Because they told him that kings would not accept any letter that has not been signed. Hence, Scholars say it is Sunnah for those who use it to sign papers and documents. And some say it is Sunnah even for normal people
Hanafi: For Rulers, it is Sunnah.
Maliki: It is permissible and recommended to wear a ring since you want to imitate the Prophet (PBUH). and Haram if you wear a ring to show off
Hanbli: It is permissible and NOT recommended
Shafi: Sunnah for Rulers and Normal Muslims
The Prophet used to wear a ring but scholars have differed about which finger should the person put his ring on because there are many authentic hadiths that tells us that the prophet used to wear it in different fingers and different hands.
1- Left hand - Maliki, Hanafi, and Hanbali
2- Right hand - Shafi
But Ibn al Qayim said: "There are different hadiths about wearing the ring in the right or left hand but all of them are authentic(correct)".
And Sheikh Ibn Uthaymeen said: "It is considered a Sunnah if you wear the ring in the right hand or the left hand"
Now this is a Hadith that answers all of your questions:
Thabit narrated that : They asked Anas about the ring of the Messenger of Allah [SAW] and he said: "It is as if I can see the shining of his silver ring, and he raised his right little finger."
Anas reported that the ring of Allah's Apostle (may peace be upon him) was on this, and he pointed toward the little finger of his left hand.
Nafi' said that Ibn 'Umar used to wear his signet-ring on his left hand.
Yahya related to me from Malik that Sadaqa ibn Yasar said, "I asked Said ibn al-Musayyab about wearing a ring. He said, 'Wear it, and tell people that I gave you that decision.' "
The ring was made from:
Anas b. Malik reported that the ring of Allah's Messenger (may peace be upon him) was made of silver and it had an Abyssinian stone in it.
The ring of the Prophet was of silver, and its stone was of silver too.
Narrated Anas: The signet-ring of the Prophet (saws) was all of silver as was also its stone.
it is permissible to wear a ring of iron
In al-Saheehayn it is narrated from Sahl ibn Sa’d al-Ansaari (RA) that the Prophet (PBUH) said to the one who proposed marriage to the woman who had offered herself in marriage to the Prophet (PBUH):
"Look for something (to give as a dowry), even if it is a ring of iron."
[Abu Dawood] and [al-Nasaa’i]
Thus it is clear that the more correct view is that it is not makrooh (discourage) to wear a ring of iron. But wearing a ring of silver is better, because the ring of the Prophet (PBUH) was made of silver, as is proven in al-Saheehayn.
However, you are not allowed to wear a golden ring:
Abu Huraira reported that Allah's Apostle (may peace be upon him) forbade the wearing of gold signet ring.
It was narrated from 'Abidah, from 'Ali, he said: "He forbade red Al-Mayathir, wearing Al-Qassi, and gold rings."
It was narrated that Ibn 'Umar said: "The Messenger of Allah [SAW] started to wear a gold ring, and the people started to wear gold rings. The Messenger of Allah [SAW] said: 'I was wearing this ring, but I will never wear it again.' He threw it away and the people threw their rings away.'"
Another thing, the prophet used to remove his ring when entering the bathroom because it was written on it (There is not God but allah, Mohammed is the messenger of Allah)
Narrated Anas bin Malik (rad): Allah’s Messenger (saw) used to remove his ring when entering the lavatory.[Reported by Al-Arba’a and it is defective].
Another prohibition is that you must not wear it in these 2 fingers
'Ali reported: Allah's Messenger (may peace be upon him) forbade me that I should wear a ring in this and that finger of mine, and he pointed to the middle finger and the next one.