Most primers can be left exposed for a long time, but need to scuffed and topcoated before you proceed with your paint job. Pick a paint brand and stick with it throught the primer and finish coat. I chose PPG. I stripped to bare metal, used DPLF epoxy primer to seal the metal, did body work on top the epoxy primer, used K36 filler primer for wet sanding, then sealed the entire car with a thinned coat of DPLF epoxy primer as a primer-sealer. As soon as I can drive it to the booth, it will get one more light coat of primer sealer right before the color.
If you don't mind driving work in progress, I'd strip and prime, strip and prime. It's a more managable project. Just use good primer, IMO.
Good luck.