Many thanks isn31c for clarifying the situation at Manchester. I always thought that a direct TPE services linked York with Man Piccadilly so it looks like that will be the case in May when the OP makes the journey. I am also not so sure that the restaurant service will be available on Saturdays if using the 12.30 from MAN > CDF.
If going via London, it should work out cheaper to split the tickets at London and note that it is not just LNER who operate between York & London (Kings Cross) but also Grand Central. London (Paddington) to Cardiff will be with GWR. Both LNER & GWR will be the same type of trains = Class 800 series Hitachi Expresses running on overhead electricity - max speed 125 mph.
If you go from York direct to Bristol Parkway it will be with Cross Country Trains and you will probably be on a Voyager Train = a diesel train with max speed of 125 mph. The 35 minutes or so between Bristol Parkway and Cardiff will be on the Class 800 GWR Inter City Express trains running on overhead electricity.
If you want to see the type of train running a particular service today, click the following link, fill in the location box and click on the train(s). Up will come a picture of the train along with the number of coaches. The odds are that you will have the same type of train. Note that some trains might be short but other trains will be on the same route at different places. Be sure to check for Saturdays as well.
https://www.realtimetrains.co.uk/search/detailed/
On the following link - the middle photo is a Cross Country Voyager:>https://www.crosscountrytrains.co.uk
You tube video of Voyager.
All trains on any route will have unreserved coaches where you just walk on and pick a seat - if available. I usually don’t book seats and just walk on and choose where to sit but that can be a problem if a service is busy. Usually, travelling in the middle of the day is not a problem. It’s not just sporting event to look out for but also music events. Beyonce is doing the stadium in Cardiff on Wed 17 May
so services will be rammed and expensive - as will the hotels. If you see a hike in the rail fares for a particular date, it is because they know something is on and demand will be high - that is to suppress demand from those who are not interested in the event and make profit from the fans..