train question - Carlisle to Haltwhistle

You can buy anytime tickets, but there are also short distance Advance Fares (on specific trains).

Depending on the train time those are between £2.60 and £3.60 each way (before any railcard reductions) and are released 8 weeks before travel.
So look at a date in mid July currently to see the fares.

Compare that with a Northern Duo flexible fare for £16.30 valid on any train after 0850 and there isn't much in it. No special railcards are needed for a Northern Duo. You can buy a Northern Duo at Carlisle on the day.

There are no assigned seats on those trains, and they are never that busy between Carlisle and Hexham. East of Hexham (which is past Haltwhistle) they get busier. I travel regularly on that line and it'll be several years before Covid since I last saw a really busy (like full and standing) train on that line. Normally they are maybe 1/3 to at most 1/2 full (if that) at most on that part of the route.

The AD122 stops right outside the station entrance.

For completeness there is also an hourly bus- the #685 from Carlisle Bus Station to Haltwhistle for £2 each, each way. That stops outside the Hospital/Public Toilets (!!) just across the road from the station- the AD122 also uses that stop as well as the Railway Station, Officially that stop is called Westgate.

thanks so much - Sounds like we can easily wait on these tickets, and maybe even take the bus!

Or you can have the Rick Steves recommended guide Peter Carney pick you up in Carlisle and take you on on tour of the wall, dropping you off back in Carlisle. It's really worth it for his expertise. See https://www.hadrianswall-walk.com/.