The credit game is a very long-term one. Unless you want to apply for a mortgage in a fairly short amount of time, there is really no point in trying to use tricks to position yourself for a certain number. The bottom line is you just need to manage your credit responsibly. Maintain low utilization (which includes trying to get higher limits), pay in full each month, and your score will grow over time. Given that, you just need to decide which cards are best suited for you.
Since your score is your biggest priority, I would recommend going with the BCP. You get a handsome introductory bonus with the PRG but it will be completely eaten by the AF after 4 years (1 year of no fee followed by 3 with annual fees totaling $525). This is assuming you plan on keeping the card for a while, though. You could get it for the MR points and cancel it later, but you will be worse off if your credit score truly is a higher priority than rewards.
Of course, we are all here because we are interested in earning rewards. That said, it is easy to rationalize paying a fee in the name of rewards. You are more interested in cash back, so may I assume you are not a frequent traveler? In my opinion, there is no benefit in getting a charge card if you aren't. You are ultimately paying that AF for the travel perks (well technically for giving up the ability to not
PIF, but you can do that on your own with a credit card and some discipline), so if you aren't traveling much it is a waste of money. Instead, get a credit card, PIF like you would otherwise have to anyway, and you don't pay anything!
Are you sure your spending justifies the preferred version of the Blue Cash? It very well may, but it is important to know the answer to this. Best case scenario: you have to spend $2,500 in groceries - $75 AF divided by the marginal benefit of the highest earning category (from merchants cateregotized as grocery stores, too, so no Walmart) - just to break even on the AF
and be indifferent between the basic and preferred versions.
Good luck with whatever you choose, though it sounds like you won't have trouble getting what you want.