Sky - Trait of Harmony. The perfect balance of all flames resulting in no contradictions and is flawless. Sky is all encompassing, which can be related to it's mysterious power - petrifaction and negation of the other six flames, BECAUSE of it's flawless state. Represents not just leaders, but the Vongola Boss.
Storm - Trait of Disintegration. The most aggressive type of flame. It's trait allows the decay and weakening of anything it touches, true to the nature of it's trait.
Sun - Trait of Activation. Increases the effectiveness and speed of any type of activities, and increases the abilities of the other six flames. Support role, capable of healing abilities through the "activation of cells" which provides for a quicker rejuvenation process.
Rain - Trait of Pacification. Rain pacifies and leeches strength. It immobilizes and calms, it can be seen as a debuffing role.
Lightning - Trait of Solidification. - The hardest of the seven flames. Because of it's impenetrable nature, Lightning flames are considered the pinnacle of defense. Lightning flames have an electrocution aspect to their flames as well.
Mist - Trait of Construction - The most abstract of all the seven flames. Basically, Mist flames bend reality through the illusions, allowing users to 'manipulate or construct' the aspects of reality.
Cloud - Trait of Propagation - The ability to multiply and replicate anything it touches, infinite and expansive like clouds. Can propagate things such as methods of attacks, weapons, ect. To project propagation, Cloud flames have the ability to leech and absorb the other six flames to fuel it's trait.
A little list I made up to help you guys with choosing your rings. :)