You can travel at certain times with just one change, at Wolverhampton. For instance, the 10.17 from Southampton will give you a thirty minute break at Wolverhampton to go to the loo, although train toilets are usually ok. Consider getting a railcard, which will reduce the fare by a third. Travel first class- it’s quieter, with more legroom, and you will get a drink and a snack. Also, split your ticket- for instance buy the S’ton to Wolverhampton ticket separately from the Wolv’ton to Holyhead, because that usually works out cheaper. The second part of the journey is particularly beautiful.
Go- it will be fun!