traveling by train to london, edinburgh and Paris

You need to look at a map. There is no direct train between Edinburgh and Paris. I would start in Edinburgh rather than having to back track through London to Paris. The best train is the train that goes between London and Edinburgh. I think it is Southern but go to nationalrail.co.uk for the schedule. Most of the rail system in Britain have been privatized so it is best to buy the tickets as early as possible for the discount. Same for the Eurostar between London and Paris.

PS Edited - Paul is correct on train - East Coast. I just drew a blank and all I could think of was Southern.

1. Best is somewhat suggestive, East Coast trains leave about every half hour from Kings Cross Station, the other option is Virgin from Euston Station with fewer departures. If you buy tickets well ahead, they are cheap enough that either service is fine.

2. No direct train from Edinburgh to Paris. The only train from the UK to Paris is the EuroStar, leaves from St. Pancras station in London, so you would need to buy your Edinburgh to London Ticket, get from Kings Cross (or Euston) to St. Pancras by either taxi, Bus, or underground (may also be a local rail connection), then your ticket to Paris on EuroStar.

3. Depending on where all you will be going, you can buy single tickets, a Day Pass, or use an "Oyster Card" (reloadable transport card) Tickets are good for the buses, Underground, and a few other transport options in the London Metro area. You may also need only the central zones or a wider range of zones depending on where you are going while there.

London buses do not take cash so you will need a contactless payment card i.e. an Oyster card, your bank card or Android/Apple pay

There are a few nonstop flights per day between Edinburgh and Paris (CDG or Orly); see www.skyscanner.com.

Actually the idea of flight would make more sense from Edinburgh - probably both quicker and more convenient - might even be cheaper. It is an easy and quick tram ride to the airport in Edinburgh.

Fly into Edinburgh, take the train to London then the Eurostar to Paris or vice versa, if possible. Otherwise, to avoid a very long day on trains, fly from Edinburgh to Paris in half the time.

If using an Oystercard on London buses, just touch the card on entering the bus. Do NOT touch out when you get off, as you will be charged again. If using it for the tube, you must touch in AND out.

Someone else needs to look at a map. Kings Cross and St Pancras are literally on opposite sides of the same street, no need for bus, cab or tube.

Thank you all for your suggestions. If we were to take a plane from Endinburgh to Paris, what is the best airline and which airports should we fly to? All so confusing for the first timer.

For Edinburgh to Paris flights, check out SkyScanner, which will show all the airlines, even budget airlines, that fly the route. For me, I've often taken EasyJet into Orly airport in Paris, but just see what times and fares are best for you. If you do get Orly, that's nice because it's smaller and more manageable than Charles de Gaulle. But either is fine.

Note that with EasyJet, you purchase a bag if you want to check one, and unless you buy a special ticket, you can only bring ONE carry-on, and they mean ONE (i.e. you have to stuff your purse into your backpack if you have one). As long as you're aware of all this before departure, it's fine.

Try to avoid any flights into Beauvais, which is an airport quite some distance from Paris.

Thanks everyone! One more question, is East Coast Trains the same as Rail Europe?

ABSOLUTELY NOT - It is a travel agency and does not operate a single train anywhere. What made you think it was the same as East Coast? RailEurope is a convenience for North Americans and tend to sell tickets that are marked up to cover their costs. Nothing wrong with using them to buy tickets for the convenience.

East Coast trains was a train company that ceased operating in 2015. Virgin Trains East Coast currently operate between London and Edinburgh.

Book tickets here https://www.virgintrainseastcoast.com/

Air France, easyjet and Transavia fly between Edinburgh and the Paris airports. Search the different companies for fares and times that suit you.

Has anyone taken Rail Europe from London to Edinburgh? If so would you recommend. The cost is a bit cheaper than virgin.

Melissa, you cannot "taken Rail Europe from London to Edinburgh", because Rail Europe does not own or operate any trains.
Rail Europe is a travel agency operating in North America reselling tickets from the companies that actually operate the trains.

• Trains between Edinburgh and London King's Cross are run by Virgin East Coast: https://www.virgintrainseastcoast.com/
• Trains between London St Pancras and Paris Gare du Nord are run by Eurostar: http://www.eurostar.com/uk-en

Both companies operate demand pricing, prices start cheap and go up (never down) the nearer the date you get. Different trains have different prices and busy trains are more expensive.
Rail Europe prices in US$, so to compare prices you have to convert currencies. But it is (re)selling tickets for the same Virgin East Coast and Eurostar trains.

thank you everyone!