Hampton by National Rail

National Rail is for enquiries, not a train. To get to Hampton Court you will need to take Southwest Train from Waterloo Station to Hampton Court. The District Line is a subway (tube) train, which doesn't go to Hampton.

Robin is correct. The instructions you found are absurd the tube does not go to Hampton Court

Hmmm, this has gotten me concerned about the directions I got from the Journey planner for going from Celtic Hotel to Windsor Castle. I'm told to go by way of Paddington, but the Journey planner takes me from Kings Cross to Hyde Park Corner with a bus to Windsor. Are both accepable ways?

The train from Paddington (change at slough) is the most convenient way. Much easier for a non-londoner. Also less susceptible to traffic delays than a bus. (this routing is discussed many times on this site you can get to Windsor (and even Hampton Court) by bus but thats a lot clumsier in most people's opinions (well mine at least)- stick with the train. very convenient and undoubtedly quicker (The country busses from London used to be green, not the regular red busses). But i havent used one for a long time now

Going by train it the best way to go takes 35 minutes...taking the bus is slow and long and takes an hr and 10 minutes. You have to options to get to Paddington Station....1st. from Russsell Square tube station take the Piccadilly Line to Piccadilly Circle tube station there you would take the Bakerloo Line to Paddington tube station. 2nd. from Russell Square tube station take the Piccadilly Line to Earls Court tube station then you would take the District Line to Paddington tube station.
Paddington train station is right there...you would want to buy a "return" ticket (that's round trip), you will have to change trains in Slough, which involves just changing platforms then Windsor is only a few minutes from there. Once you get to Windsor as you exit the train go to your left and walk up to High Street and you will across the street from the castle.

The Travel Planner can be more sophisticated or more stupid than its should be depending on what parameters you put into it. By bus going to Hyde Park Corner then getting the Green Line bus to Windsor is perfectly feasable A Day return on the train is 9 or 12 GBP (peak, non-peak), on the bus (Green Line) 9.50 / 13.50 GBP. Train is also about 20 minutes faster, though going onto Hammersmith and getting the bus there, not Hyde Park reduces this further as the bus goes staright onto the motoway from Hammersmith. Both services stop in Slough, before Windsor with the train you have to change trains The journey planner also accounts for known tube closures of which there are a lot at weekends currently, so some recommended journeys can look a bit weird at first. Most people will use the train (the bus is only an hourly service) and the train isn't delayed through road congestion, although you no doubt will be travelling against commuter flows with little/no problems.
The buses have free Wifi so you can catch up on messages and use the time travelling more profitably.

i am tempted one day to take a train to Hampton Court and the Green Line bus back- just for the change (coming back i am more comfortable that i will recognize where i am). I was thinking of doing the same for Windsor until Bob said it is all motorway- no fun in that

I think you are getting confused between Windsor and Hampton Court. Hampton Court has no Green Line buses. The only viable direct option to Hampton Court is by train from London's Waterloo Station. The station at Hampton Court is on the other side of the bridge over the River Thames to the Palace. If you want an native, its to use the river bus service that runs in the summer months. I thinks its 3 or 4 hours if you go the whole way from Hampton Court to Westminster Pier opposite Big Ben. Most people will just go as far as Richmond and get the Underground from there. The summer timetable isn't published yet, but when it does it will be linked from here:
http://www.tfl.gov.uk/modalpages/15544.aspx