The Bible is full of internal contradictions and external contradictions with the religions that were purportedly developed in conjunction with it. In order to make your way through its contents do your best to set these aside and take the texts at face value as best you can. The only practical critical lense you should attempt to apply upon first reading is What aim, theme, or message is being presented here? I think pursuing the countless number of seeming contradictions is problematic for a few reasons. One is that it will be terribly distracting; there is a lot to get through and in addition to prolonging the endeavor you’re likely to be distracted from the thrust of each story if you pursue these apparent contradictions. Second, if the attempt is to explain away the seeming contradiction and reestablish the often supposed “harmony of scripture” the attempt [at least from my perspective] is in vain. None of the texts claim that such a level of harmony ought to exist, or that the presence of these contradictions discredits the claims of the texts. Its only through external traditions that such a view of these texts has been produced and the sheer number of contradictions and lack of self contained denial of their existence suggests there is little to gain from establishing a “harmony of the scriptures”.
Critical studies of the texts in light of their incongruences, as well as their conflicts with the popular tenets based on these texts is a useful and important exercise but it’s impossible to conduct without giving the texts and their traditional groupings within the particular religion your studying (ie. The Bible and Christianity, or Judaism and the Tanakh) an honest and complete reading.