I have some information about those rings ^^
Rings were drawn from ancient Chinese and Japanese lore, the kanji on each ring have served in the past as representations of Gods, to help in concentration before battle and in protection from evil. Their ring placement on their finger corresponds to their position on the summoned statue, with each member wearing the ring on a different finger. The rings seem important to each member, as Deidara was set on finding his when it was lost. Orochimaru also took his when he left the group, which apparently denied the group the ability to replace him with someone new. With Sasori's death, Tobi was eager to get his ring and join, but he would need to go through their entrance requirements first.
and for members:
1-Pain
Ring: Rei (Zero)
Finger Position: Right Thumb
2-Deidara
Ring: Sei (Blue-Green)
Finger Position: Right Index
3-Konan
Ring: Byaku/Haku (White)
Finger Position: Right Middle
4-Itachi
Ring: Shu (Scarlet)
Finger Position: Right Ring
5-Zetsu
Ring: Kai (Boar)
Finger Position: Right Little
6-Orochimaru
Ring: Sora (Sky)
Finger Position: Left Little
7-Kisame
Ring: Minami (South)
Finger Position: Left Ring
8-Kakuzu
Ring: Hoku (North)
Finger Position: Left Middle
9-Hidan
Ring: San (Three)
Finger Position: Left Index
10-Sasori
Ring: Tama (Sphere)
Finger Position: Left Thumb
11-Tobi
Ring: Tama (Sphere)
Finger Position: Left Thumb
Hope that i helped you ^^