Hi there and
to the forums!
You've come to a great place to learn even more about budgies! You have been given great advice above.
It's great to keep them in the living room, as that's where the people tend to hang out. However, you can always pin up a sheet in the doorway or something similar to make the room a bit smaller and closed in if you can't move their cage.
It's important not to force them to come out if they don't want to, as FaeryBee said, their cage is their safe space so it's normal for them not to come out.
My girl is also scared of big, new toys/things, but if I keep it by her cage long enough and interact with it (like touching it and making excited noises, putting one of her favorite toys by/on it, putting treats near it) then eventually she warms up to it
Be sure to read through all of the links above, which include the many articles and stickies that we have here! If you have any questions after reading through everything, be sure to ask as we'd love to help.
Please keep us posted on how things go! We'd love to meet your budgies when you get the chance