I've been playing through the RE series lately and I did the originals followed by the remakes and then did the tie-ins (i.e. outbreak) and yeah... the remakes felt very different from the originals and don't really sync up with other canonical material unless you look at it as a "broad strokes" kinda way.
I think Resident evil 0/Remake 1 should be treated differently though, as the Umbrella/darkside chronicles definitely treat these two as canon, so they likely share canon with both the original timeline and remake timeline, if that makes sense. Not to mention REmake 1 is a much closer adaption of the original game than the others are.
Personally on a playthrough I think it would be best to do all the original games up to code veronica (so Re1,2,3 maybe Outbreaks, Survivor, CV) and then do RE0 and REmake 1, as RE0 also opens with some text referring to the events of all of those games