Very little difference between first and second class in my opinion.
If you can pindown travel times, I recommend that you book your tickets in advance. You can do this on The Trainline.com and then pick up the tickets at a UK train station.
On certain routes trains can be crowded. For instance last year both in July and November, I took a train fom Oxford heading to Manchester. Both
times the trains were crowded. But I had booked in advance and reserved seats. When one time, I found someone sitting in my seat, I just showed them my ticket with the seat reservation and they got up.
If you don't want to book now (with cheaper fares available), at least don't wait until the last moment to buy your ticket. Walk-up last minute fares ae the highest and you may not get a seat. At least try the day before or preferably a few days on busy runs.
However, how crowded a train will be will depend on the route. And you can't get reservations on local short distance trains. For instance if I buy a ticket from Oxford to London, there are no reservations available. The only time the local trains will be very crowded is during commuter hours.
Another time I took a train from Reading (Berkshire)
to Southampton early on a weekday. It was a train headed to Bournemouth and it was crowded. There were no reservations on this train. I only took it as I had to make a flight from SOuthammpton to Avignon.
Trains from Reading to Gatwick Airport do not offer reservations and I have never had a problem getting a seat. However, the Gatwick Express from London Victoris can be VERY crowded with no reservations.
Hard to predict when you can get reservations, but I know that the route to Birmingham and Manchester is
very busy since these are important business towns.
Hope this gives you some ideas. Perhaps the UK members will chime in with some more information.