Advanced train ticket purchase while in the United States

Choose the collect at station option - you'll get a code to collect a ticket from a self-service machine at any train station.

No price difference.

In the final stage of purchase (if direct from GWR) you get the options for ticket delivery, you can select to collect them at the staion in which case you get an email with something like an airline booking code. You go to a GWR ticket machine at Paddington, there will be an obvious place to press for collection, it asks you for the code and probably for your payment card as proof of iD, then it prints real tickets - all the tickets on that booking, so for a round trip you don't have to do it twice. If you buy from a 3rd party reseller like Trainline you should also be offered collection at station but they may charge a fee for this service - which they don't actually provide because GWR will be doing it!!! The collection process takes about 60 seconds so you donlt have to be there way in advance of departure

We purchased tickets ahead of time from the U.S. we followed the link from national rail.uk which took us to the train provider, GWR (your trip may vary). We were issued digital tickets which we could display on our phone, or print ahead of time. We took printed copies as backups, but generally used our iPhones (add the ticket to your Wallet). Not sure about CDMA vs GMs, as I don’t know what that means.

If your day is set in stone, it's a good idea to buy advance tickets, they will be less expensive than walk up fares. You just need to be aware that Advance tickets are for a specifically timed departure, you will be unable to use it on an earlier or later departure, only the time on the ticket. Unless of course your train is cancelled or delayed.
All train operators sell each others tickets as well as their own. So you could book tickets with a company in say, northern England for tickets in the South East. I do however think it's advisable to use the App or website of the company that operates the train you will be using. Makes things easier in the event of delays or cancellations. In your case, if you are having problems with GWR, you could use another company.
Once you pay for your tickets, you are normally asked the type you want, paper or digital. The latter is very popular these days as they are stored on your phone. If that is not possible, select paper, and once you arrive in the UK, go to almost any station and follow the prompts on the ticket vending machine to collect tickets. You'll need the card with which the payment was made and a reference number that you will have been given for the purchase. The tickets will be dispensed from the machine. Wait until everything has dropped, you seem to get a lot of paperwork for two tickets.

Thanks for the information everyone.

You may well not be asked for the credit card used for purchase; I've picked up quite a few tickets in England over the last month and have only needed the confirmation code displayed at the time of purchase. It's possible the requirement varies, depending on which company's ticket machine you use (any will work) or the cost of the ticket(s); my purchases were for single tickets and were not terribly expensive.

I think that the requirement to input a credit card to collect tickets depends on the age of the machines you are using. I most often use the machines at Preston run by Avanti and have not had to put a card in for several years now.

On this route on a summer Saturday I’d be amazed if you can make any savings by booking in advance. It’s a popular route and the trains are usually busy. It’s worth booking to get a seat reservation but don’t expect any bargains.

I buy tickets online using the train company's app. I then get the ticket in the app. (What's important is the QR code.). I then take a screenshot of the ticket just in case my cell service conks out when I need to dispay it. You don't need cell service to display a screenshot.