Train tips from London? Return tix? Region Rambler?

There are no integrated bus/train tickets for Kent.

There is a 3 day Kent Rover Rail Ticket- https://www.southeasternrailway.co.uk/tickets/ways-to-save/kent-rover

For the day trip just buy an Off Peak Day Return Broadstairs to Chatham on the day. You can break your journey as many times as you want in each direction on that journey. That is £27.80 before the 1/3 railcard discount. (Broadstairs to Chatham)

I am ambivalent on taking the slow train or HS1 on the outbound journey. Both are good quality trains, but others will tell you inaccurate stuff on the quality of the slow trains. To me it's half a dozen of one and six of the other.

I would buy an Advance Single on the outbound journey, and a through Advance Single Broadstairs to York on the way back- for the protected connection that gives you at St Pancras/KC- it is the sum of the two fares, so no cheaper and no more expensive.

Don't forget that £2 single bus fares are still in force. Stagecoach- the main bus operator in the area have a £9.10 South East Day Rider ticket. You would need to do the maths to see if that is better value than the £2 fares.

trains from Broadstairs go to Ramsgate and Margate on the coast, to London Victoria and to London St Pancras International.

Between Broadstairs and from Victoria takes around 1:53, to and from St Pancras alternates between 1:22 and 1:43, so convenience is probably a major factor on the way to Kent and the trip to York is a slam dunk for the high speed Javelin service into St Pancras as the trains to York go from across the street from St Pancras.

None of the services between Broadstairs and London offer a First Class option, so either route it will be Second Class.

The Javelin trains have more luggage space but both work fine.

On the District Line, Victoria is 7 stops from Hammersmith. On the Piccadilly Line, Kings Cross St Pancras is 13 stops. And on the Hammersmith & City and Circle to Kings Cross St Pancras is also 13 stops. So you pays your money and takes your choice.

Stuart & Nigel:
Thank you so much for your clear, detailed explanation and expertise. I wouldn’t have thought of the potential delay/connecting train issue if I had bought the London-Broadstairs return ticket. Good point. I’ve made notes of your times/stations and connections. You’ve both prepared us very well, to be confident of our plans for this train trip. Many, many thank yous!

Today the schedule opened up, so we purchased our train tix STP to BSR. 12:40-14:03 for 20GBP (with the two together rail card).
This is hubby's first trip abroad, so we wanted to give him the "fast train" experience. We'll give ourselves lots of lead time to get from Hammersmith tube station to STP on Monday, and maybe time for a coffee/snack at the station.

Next we'll look for Broadstairs to YORK
Any ideas what a good price might be for the advance singles?
Mid-morning Thursday 20 June. [if I split the ticket, we won't be protected if delays, correct?]

Preference for Grand Central vs LNER?

Thanks for your time and expertise! :)

The previous Thursday, with a railcard the fare is £41.25 on the 1027, 1127 and 1227. Something around that is around right. The 1027 seems to be the cheapest train most days, but fares will fluctuate a bit depending on LNER demand.

That fare is 50 pence less than the sum of the parts!!

Buy in 2 parts and you are not protected if there is late running. On LNER vs Grand Central LNER run 2 or 3 trains an hour to York, Grand Central about half a dozen a day. Apart from the fact that you can't book a through fare onto Grand Central if they cancel a train then you have a long wait for the next one GC almost always run full as well so you could end up standing.
I know what you are saying that on the 1256 Grand Central are half the LNER fare at £15.50 versus £31.50 on the 1230 LNER.
Personally I really like Grand Central seats (and the overall product) far more than LNER, but the catering offer is more basic, and Grand Central run diesel trains rather than electric on LNER. Also some people (and I am inclined to agree) think that the GC cars run quite roughly at full speed due to their age.
Essentially you get what you pay for and the choice is ultimately yours.

For me thinking of a visitors best interests a through fare onto LNER is just far superior in all respects, but that is just my guidance.

Stuart! Thank you so much for your insider perspective once again. We will indeed book the SE & LNER from Broadstairs to York.

I will book with “extra” time for the London connection STP - Kings Cross since we have to change stations. I think it is only 20 minutes and we don’t mind a little breathing room.

Have a lovely day :)