What I thought of doing is chopping the weeds down to ground
level, then covering it with a layer of manure followed by old carpet
or black plastic then coming back later and digging it all in.

Digging in carpet or black plastic sounds a lot of work. :-)

But apart from that, sounds ok, although I wouldn't bother digging it in.
But then again, I'm a fan of no-dig anyway.

Does this sound OK? Is there anything else I should be doing? Maybe
add some lime with the manure?

Depends on what your soil is like, and what, if anything, is missing. Get a
soil test kit and find out what it needs.

In the meantime, you've got time to think how you will design your lottie
and what techniques you will use. Eg raised beds and paths, no dig,
'traditional' rows, organic, etc etc.

Best,

- h