Best Web Site to Purchase Rail Ticket for London-Cambridge?

Any train operator can sell tickets in any route, so it really doesn't matter which train operators site you used for booking. I believe it is ThamesLink that operates this particular servuce.

I usually go with one that operates the route (in that case, ThamesLInk) but Simon is correct in that you can use either.

I do suggest downloading the ThamesLink app so that you have the ticket on your phone and all the information right there.

Sorry to see that you are only doing a daytrip to Cambridge ( I've made two weeklong visits there , and would gladly go again , so much else to see there ) But for your enjoyment , you might like this film from the eighties ( from a story by Jefferey Archer ) . Quite a touching tale set in Cambridge - https://youtu.be/Y2YIKQ5T1dY?si=p7bv99gTNKF1qWB3

Thanks for your guidance! I did not know that ThamesLink operated this service. I will book with them and add their app to my phone.

Alas my time in England will be short--just three days in London, following an eight day trip to Egypt. Maybe another time I will be able to manage an overnight stay in Cambridge.

From the train timings and the departure station in London, also the journey times I can see that these are actually Great Northern trains, not Thameslink, and the outbound train leaves at 8.24, not 8.42- no train can do the journey in 31 minutes - that's the immediate giveaway.
At Kings Cross you will be looking on the departure boards for the 8.24 to Ely (the trains final destination).
Cambridge is first stop on that express train.
It will probably change on the day, but it is meant to leave KC from Platform 7.

But the above about ticket purchase stands.

Thameslink leave from St Pancras, and are slower, hence why these trains can be recognised as Great Northern, prior to checking.

Thank you for clarifying, Stuart. Yes, I transposed the numbers on the London departure time; the train leaves Kings Cross at 8:24, as you noted. I will purchase my ticket via Great Northern and look for the train to Ely as the final destination.

In New York, some commuter rail stations are quite small with a short platform, so only some of the carriage doors (for example, the front four cars) open at the station. Does something similar happen at Cambridge, or is it a "full size" station so that all doors will open, and it does not matter where I sit?

Cambridge especially is a very long platform. Your train will probably be 8 or 12 cars long which the platform can easily take. All platforms on the Great Northern main lines can take full length 12 car trains AFAIK. Some north of Ely were lengthened as I recall when the line was electrified, oh 30 years or more ago.
But there are lots of short platforms round the system. Mine in Cumbria is one, it can only take 2 cars, even though we have 4 car trains sometimes. In Scotland there are at least two stations less than 1 car long, so only the front door can be opened.
On my own line we sometimes used to double or treble spot when we had 10 or 12 car excursion trains- stop the front cars on the.platform, use those, pull forward then the next cars etc. A very inefficient and slow way to work.

all platforms at Cambridge accommodate one or more full length trains.

The very very long platform nearest the booking hall at Cambridge has various designations depending on where you are - and are well signed. That is variously known as Platform 4, Platform 1a and Platform 1.

Leaving Kings Cross station the gates to the platform are at the very back of the train. I tend to wander up before the train leaves and settle into an empty or emptier carriage - these will be further from the gate because by nature people tend to be lazy and hop into the first few doors. Returning from Cambridge many will sit at the front because it will be the shortest walk into Kings Cross on arrival.

You can just as well use the Thameslink app for those tickets, they are the same company as Great Northern under the skin and the app based on my fairly extensive experience works very well.

You could save just over one pound by buying Single Advance fares but that would tie you to particular departures - the Anytime allows just what it says, any train on that route out that day and any train back. You could have an earlier breakfast and go earlier if you like, or go to Fitzbillies in Cambridge for breakfast and get an even earlier start.

These Anytime tickets don't go up in price. There is no really good reason to get them 2 months ahead. They will be available on the day and same price. Just use the app when you wake up, or the night before. Then if you get sick and can't go, no sweat.

Thank you so much, Stuart and Nigel. Stuart, I find quite charming the idea of a wee Scottish town with a station platform less than one car long! Nigel, I appreciate that you said the Anytime ticket will not change in price. I would prefer to stay flexible with my plans--hopefully not because I could feel unwell, but because serendipity might provide me a better option for the day. It would not kill me to miss the Fitzwilliam's exhibit because I will be coming to London after visiting Egypt.