Langstroth hives look like a bunch of stacked boxes. They allow bees to build vertically - sort of the way they would in a hollow tree. These are easy to expand - all you have to do is set another box full of frames [called a super] on the stack. However, the supers get heavy if they're full of honey and that makes them hard for a short stout woman with no upper arm strength to lift off in order to get to all areas of the colony.
Top Bar hives look like a long box set on a set of sawhorses. [They're usually not, but that's what they'll remind you of.] Top bars allow you to have easy access to all areas of a colony, but they don't have the expandable space that the Langstroth's have.
Here is a pic of our new Langstroth hive. It won't stay in the living room, but that's where we put it together. We haven't decided exactly where to put it outside yet.
In the meantime, K2 is in charge of painting the supers, base and outside cover. We'll start that today.