"Rigid" means what you think it means. I have an Ansco 8x10 (post-WW2 model with front tilt) that's as rigid as you could want. A lot depends on the tripod. Deardorffs are lighter but more expensive. The weight and folded size of the Ansco -- a tailboard design vs. the Deardorff clamshell design -- are its main disadvantages. I don't know how heavy the Burke & James models are. Ansco cameras are not inferior to Deardorffs; Ansel Adams is known to have used them.
5x7 offers a smaller choice of film emulsions. Figure in the cost of a suitable tripod and of course a lens (or lenses) and possibly lens boards as well as film holders etc.
Also -- what kind of photography are you planning to do? If the camera doesn't have a long enough bellows draw, tailboard extensions (for close-ups and long, i.e. not telephoto, lenses) for a specific camera are not easy to track down. My Ansco came without the extension, which limits the bellows draw is to about 26 in., adequate for a 300mm lens (normal for 8x10) or a 250mm moderate wide-angle. The minimum focus distance is around 24 in. if I remember right. I do mostly landscape for which my outfit is just fine. There is an excellent large-format website with members who are happy to answer questions from beginners:
Agfa Ansco and Ansco are just different trade names for the same cameras. Ansco separated itself from the German Agfa company during WW2, so the Agfa Ansco models are older.