DNA is pretty stable, so you should not worry. I have kept DNA in the fridge for years. The best way to keep it is in TE buffer for long term storage. Low-TE buffer with reduced EDTA concentration is preferred if your DNA concentration is low and it is going to be used for sensitive downstream enzymatic processing. DNA is also stable stored in DNAse free water in -20*C.
I agree that DNA is stable enough to store for a long time at -20oC, but I have noticed that aqueous solutions tend to evaporate from the surface and condense as frost at the top of the container over the course of several months. This causes the surface of the solution to dry out, which may not be good for the DNA. Therefore, I would recommend -80oC for long-term storage.
Extracted gDNA can be stored days to easaly a week on the bench, months t years at 4 degrees and I think pretty indefinatly at -20. Just avoid repeated thaw freezing as this sheers and unpredictaly breaks your bulky gDNA. Also the good Buffer from above is good advice. Check pH and keep it at aroun pH 8. Acidic conditions will destroy your DNA.