what is the rationale for choosing the criteria to identify DEGs ( absolute logarithmic fold change |log2fc|>1 and adjusted p-value (padj)<0.05)?
I think the numbers you cite are the most extreme values that people will still accept. In most cases I would go for lower p-values (at least 1e-3).
As to how to choose your thresholds, it depends on how confident you'd like to be versus getting a reasonably good number of DEGs. Think of it as two knobs you can turn in either direction to adjust the output. Increasing the |log2fc| and decreasing p-values has the effect of reducing the number of DEGs.
How these cutoffs are adjusted is sometimes determined by practical reasons. If one applies your cutoffs and gets 500 DGEs, for many people that would be more than they wish to analyze. Slightly increasing |log2fc|, or slightly decreasing the p-value, or both, will bring down the number of DEGs. It is good to be principled and always stick with fixed thresholds (say, |log2fc| => 2 and p-value =< 1e-5), but experimental outcomes often are not what we expect, and most people I know apply variable thresholds for both parameters.
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