debating whether getting advance tickets makes sense

Advanced tickets are definitely the cheapest way to go if you have a fixed itinerary. If you get an advanced ticket it is for only the train you booked. Don't show up and the fare is lost. You can not change your ticket ever for any reason. At least my father-in-laws passing away didn't seem to rise to the occasion. I have had trouble reserving tickets with my Visa credit and debit cards but the MasterCard worked first try. You must claim your ticket at an automated ticket machine at a train station with the same card used to purchase the ticket. I had some tickets that I thought were only able to be collected at the machine and we ignorant Americans (especially Pennsylvanians since I was once one) can not just saunter up to a ticket window and pick them up there. Of course, as an ignorant American I might have been mistaken but it's not that hard with the usually helpful Brit standing around. My advice is to really, really understand what you need to do and the restrictions before buying the tickets.

The cheapest fares are on the 'Advance' tariff, which are available from 12 weeks before travelling through to the day before. Generally they get more expensive nearer to the date and they can sell out. The disadvantage is that they are valid only for the specific train for which they are booked, although you can change them until as late as the day before. Senior Railcards cost £30, you would need one each, and they generally give you a 33% discount on off-peak fares. As you'll see below, for some types of ticket they won't save you money overall. So, here are a few comparisons of the total costs with and without the Railcard, starting with more flexible 'Anytime' and 'Off-peak' fares. Without a Railcard - Cheltenham to York 'Anytime' = £166 for both of you. York to London 'Off-peak' is £103 for both of you, if you don't mind catching the 10.27 departure. So that comes to £269. With a Railcard - the same trains are £109.60 and £68, plus £60 for 2 Railcards, totalling £237.60 Without a Railcard - 'Advance' Cheltenham to York on the 10.11 departure on 12 September (but buying that ticket today) is £82 for both of you. York to London a few days later on the 10.27 departure is £75 for both of you. Total £157. With a Railcard - same dates and departure times, same 'Advance' tariff tickets cost £54.10 and £49.50 plus £60 for 2 Railcards, totalling £163.60. If your itinerary is certain and you are sure you can catch specific trains, then clearly the cheapest option is to buy 'Advance' tariff tickets as soon as possible. Cheltenham station has the facility to collect pre-purchased tickets either from one of the ticket machines or from the ticket counter, just leave enough time to do that and collect your York to London tickets at the same time. You can check my calculations by using the journey planner on www.nationalrail.co.uk

Thanks Kevin, your analysis indicates that I should look into advance senior tickets. I can't say how much I appreciate your help. And this Travelers Helpline in general is just GREAT!
Betsy

You can usually change your booked journey with advance tickets so long as you do it before the time of the train you have originally chosen (practically this means the day before as Kevin has said above, although there are some exceptions). If the fare is greater than originally paid you need to pay the difference plus £10. If it is less you don't get a refund of the difference and the £10 is still payable. Print-at-home tickets can be less flexible and come with their own T&Cs. Cheltenham to York is a Cross Country Trains route - these tend to have pricey advances in my experience so if you see a good price that suits, I'd jump on it.

Marco has clearly confirmed my two key points. First, there are many things to understand about the advance ticket purchase and they may not be obvious to us infrequent users. Second, you can always count on a friendly Brit to help you out.