Hi Scott, http://www.seat61.com/ has a lot of train info. My first time on trains I used a BritRail pass, so I would not have to worry about tickets. I also purchased a first class pass b/c while I will likely never fly first class, I could afford the difference with rail pass. Many say that the train gets everyone to the destination the same time, true, but it was lovely :-) The best trains for first class were Virgin, I found, in terms of food served.
How long is your trip? That could help decide the itinerary. A shorter 8-10 day trip, I'd likely do some days in London, head north for an overnight in York, continue for some days in Edinburgh, then fly to finish the trip in Dublin. Cheers.
FYI .. the BritRail pass has convenience, pinning down the itinerary and doing point-to-point tickets, purchased in advance can save money. The London-York-Edinburgh goes up the east coast and means no Virgin trains, but perhaps the London-Lake District-Edinburgh would mean Virgin trains all the way and you can use advance fares to save money or a rail pass for convenience, though if you know the train that you'd likely use, make a reservation (they're free) to be sure of a seat. I had no trouble with most trips, but one trip had a full car.