London to Edinburgh travel

The sleeper train option is what I did. You can store your bags at the train station and take in some sights before getting a good night’s sleep in a sleeper car which I had to myself. It’s better than wasting a precious day traveling.

If you are at the airport it makes a lot of sense to take a flight. Otherwise it is a good hour just to get from the airport to Kings Cross. For others, this is a good example when an open jaw ticket -- into Edinbugh and home from London -- makes a lot sense. Big time saver.

Are you planning on spending any time visiting London, or elsewhere in England? If Scotland’s the vacation destination, and London is simply an airport connection point, you could fly to and from Edinburgh, with that London connection on each end. You’re already at the London airport . . .

We will be traveling around Scotland for 2 weeks in September and will
be flying in & out of London. What is the best transportation option
to get to Edinburgh? Taking a hopper flight would be a different
airline.

I'm not sure what a hopper flight is, but which airport and are you planning to go direct to Edinburgh from the airport?

If we take the train, would we need to take the tube from the airport
to Kings Cross Station? How long should I plan for?

If you buy a flexible train ticket (Anytime or Off Peak), you don't need to plan for any time at all. You just take the first train to Scotland when you arrive at King's Cross, they depart every 30 min.

The train from Heathrow to Kings Cross will take about and hour. The trip from Kings Cross to Edinburgh is a little under 5 hours. You can check departures and pricing at the northeastern railway site.
https://www.lner.co.uk