As far as a one day hopper goes I think it's the same price wherever you go. I would buy it online to save the hassle (and precious park time) of going to the ticket booth.
They email you either a voucher that you take to the ticket window or one that you can take directly to the gate. It's been a while since we used way.com so I can't remember which!
You will have the option of hard ticket (add'l charge ) or emailed voucher (free). You can take either one right to the turnstiles if purchased through Disney.
Yes, they scan the bar code on the voucher right at the turnstiles and hand you a regular card/ticket in exchange. We've done this several times recently with military vouchers purchased at our local base ticket office.