For longer periods of time it is always advisable to store your DNA at -20C. Regarding solution for storage, some recommend TE buffer and some advise nuclease free water.
4C is more than suitable for long term storage. However, most people worry about nucleases degrading their pure DNA or a lack of long term stability at temperatures above -20C. However, the additions of EDTA and Tris easily solve this issue. EDTA chelates divalent ions (rendering them inactive), which are common in nucleases. Tris will act as a buffer in the DNA's local environment and keep it stable.
In general, there are four broad strategies for long-term DNA preservation:
Room temperature on a ‘dry’ solid matrix
–20°C
–80°C
–196°C (storage in liquid nitrogen)
Two of these methods, dried and stored at room temperature and storage at –196°C, share a common mechanism where the DNA is maintained in a glassy (or vitreous) state. In the glassy state, molecules lose the ability to diffuse such that the movement of a proton is estimated to be approximately one atomic diameter in 200 years, thereby preventing chemical and nuclease degradation. If moisture is added to the ‘dry state’ or the temperature is raised above the glass transition temperature of water, movement and reactivity of protons is re-established and damage to the DNA can occur .
I store genomic DNA at 4•C, plasmid DNA at -20. Regarding the buffer, I recommend ito use just Tris to keep the pH buffered, and avoid spontaneous hydrolysis of bases