Correction for multiple regression models: Holm's vs Hommel Procedure

Hi All,
I am helping a colleague conduct some exploratory regression analysis on some data. She is running a series of multiple linear regressions (about 20) to see which model predicts her continuous DV best. We discussed that she should consider controlling her Type I error rate using a modified Bonferroni correction.

I’ve done some reading to know that the Holm’s procedure is better than the traditional Bonferroni correction and the Hommel procedure is better than Holm’s. However, much of the reading I have done has suggested that the Hommel imposes “additional restrictions on the distributions of the test statistics”. Do any of you know what types of restrictions it imposes? In other words, what are the assumptions of the Hommel test? How do I determine if Hommel or Holm is better for reducing the Type I error rate for the proposed exploratory regression analyses that my colleague is conducting? If it helps to provide context, we work within the field of psychology and education. Any feedback would be much appreciated.