EDIT: Found it, but it only says 777 or 787. How do I know if it is the 1-2-1 or 2-4-2, etc.?
ORIGINAL POST:
I gifted my elderly mother for Christmas a cruise out of Southhampton to Denmark and Norway. (Her father was from Denmark and she has never been. It has been a lifelong dream of hers to go there.) We will be flying IAH to LHR. My mother has some mobility issues and experiences a lot of back pain so we will be flying either business or first with the lay flat beds. The only flights they have first on would require us to fly in earlier and fly out later than what I would like. However, if a flight has the new business club suites (or whatever they are called with the 1-2-1 layout in business), I don't see any reason to do first. How do I tell what plane they are using before I book?

Also, does BA offer any help getting through the airport for someone with a walker or wheelchair? Is the pre-flight service better or different if we do first rather than business? I am a little concerned about handling our luggage and her.