The question "Which BritRail pass should we buy?" is just like the famous trick question, "have you stopped beating your wife?" Before answering that, you have to know, does the person have a wife, and did they ever start beating her.
Similarly, the first question isn't "which railpass," but "will a railpass be better than point-to-point tickets?" These days, the answer is often NO, but of course it does depend on all the particulars of your situation. So, wait until you've decided on an itinerary before you make a decision on passes. And before you do buy any pass, read this from rail guru The Man In Seat 61 and make sure you understand all his points: https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#railpass-or-point-to-point-tickets
Next, you've made a common first timer "mistake," which is to think that since the UK is so much smaller than the US, you can see lots of it in a short amount of time. You can't. Your proposed itinerary will involve a lot of time lost to travel within the UK, and with only 10 days, that's not the best use of time.
If you do insist on trying to see England and Scotland in 10 days, you should fly into London and out of Glasgow or Edinburgh. If you have already purchased flights into and out of London, stick with England only; there's plenty of natural beauty without having to go to Scotland. Let us know if you already have flights, as that will determine the rest of the advice.