There is no universal rule for this threshold. You have to make educational guess based on your exp design and your target/hypothesis. Starting from log2FC = 0.26 up to 2, I have seen in the literature.
There is an interesting discussion on this forum regarding this, you should read that one for more information.
Irrelevant note: you can select genes based on p-value rather than log2FC, which is, statistically speaking, a slightly better measure.