I've never run 5e and only played like one game in it, but my advice would be to either leave the classes alone or slightly adapt existing ones - making classes that are distinct enough but still balanced with existing ones can be very tough, and a new campaign isn't the best time to be play testing them.
I've done a fair bit of world building for other systems and everything else you've brought up - races and monsters should be pretty simple. Just keep a keen eye on balance and make sure everyone is still having fun; sometimes things don't translate well from literature to rules either, so that may require some DM fiat.
As general advice, if this is a world you are writing and keen to show off to the players, make sure you don't fall into the trap of trying to railroad them into doing the things you want them to do, if they are the PCs, it's their story - no matter how cool the things are that you want them to see/do, don't try to force it.
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