How much time/how many opportunities will you have to get out and hunt? The less days, the sooner I shoot. For years I had very few days to hunt rifle season in PA. I usually had 1.5 days for buck (1990-2005) and maybe the same for doe, which was three days after the two-week buck season. I shot the first legal buck I saw, IF I saw one. For doe, same, first I had the chance at. Multiple years I was able to harvest two in that day+, sometimes two in the same day. This was private land.
The last few years I am lucky to have a small property that allows me to hunt 400+ hours a year from archery to late flintlock. I am much more patient now because I can 'afford' to be with my time. I enjoy watching the deer and learn something every time out.
I choose to not shoot doe early because I want the chance at a bigger buck and the best way to ensure opportunity is to keep your local doe alive through the rut. Usually I am not shooting doe until the second week of rifle season, if I have not taken a buck up to then. I would rather try for a doe in flintlock season after Christmas. Personal preference although much harder to do. If I am invited to hunt elsewhere or decide to try some state game lands or parks, i will take the first legal deer seen.
The opportunity to be out is special and only you can decide what you shoot and when. Recognize that power you have as well to take a life. Sometimes letting that deer walk away is more rewarding. If you are pressed for days and hours, then make the most of it and take the best shot you can.