Before we moved here I called my credit union and asked several questions, pretty much the ones you are asking: what is my daily maximum amount I can withdrawal from an atm and what is the maximum amount I can charge to my debit and will it be the same amount times two (cause dh and I have a card each). I also asked what is the charge for using my debit card at the atm and at stores.
Also, definitely make sure to tell your banks that you are coming over here and that you will be using, even if you don't plan to use one of them.
Using your debit card will be no problem. What I usually do (sometimes I still have to do this because my Barclays debit card messes up), I tell them that this is an American card. So they know they have to swipe it. I can't put it into the hand held thingy where you put your British debit card.
Also, just like you said, I would withdrawal money using my American debit card and then turned around and deposited it to my new Barclays account. Finally I called my credit union to see if they did money transfers and how much it would be. For me the $8 my credit union charges is worth it rather than having to go to the atm machine to take out money.
And one more thing, I liked that w/the Barclays debit card we could change our pin code. They gave us an initial pin code of course but then we could easily change it by going to a machine. So that way you can choose a number that you are already used to, if that is what you would like to do.