I played resident evil series many times in chronological order and when I arrive at resident evil 1 I always play both scenario since both of them are Canon you cannot ommit one or the other, you had to play both of them, you cannot play resident evil 1 and play olny one scenario since later game reference event happening in both scenario...
Well you need to play both as you can't get the actual canon ending where all four STARS members survive.
Jill's scenario shows that Barry survives and is necessary for the overall timeline as he reappears in RE3 and REV2.
Chris' scenario obviously has Rebecca (and thereby links it to RE0) and shows how she survives, which is also necessary as she reappears in RE: Vendetta.
In addition to that, RE1 is also where Wesker’s hate for Chris begins. This hate continues in both CV and RE5 and is very important.
In conclusion, the canon story of RE1 must be a mix of both scenarios. But if I had to pick only one, I'd pick Chris' campaign as it adds more to the overall story.
It's Jill for me, but since there is no ending which shows all 4 of them (Jill, Chris, Barry, Rebecca) making it out alive its difficult to say which one is more fitting for a timeline playthrough. Why I choose Jill comes down purely to personal taste, and to me she feels more like the main character for the classic games before Leon became the poster boy of the series.
If they remake the RE1 remake (which I personally don't think is needed, but apparently there are some fans who'd like to see it remade in RE2 remake style) Capcom would get a new chance to reimagine the ending so that its possible to unlock an ending that shows everyone making it out alive in the helicopter.