Train reservations

You don't really need to make reservations ahead of time, especially on routes that aren't high-demand i.e. London-Edinburgh. If you're really concerned about it or need to be on a specific train at a specific time, reserve at the ticket office when you arrive in London for Wales, and Aberdeen when you arrive in Minffordd. Check out nationalrail.co.uk for more information about reservations and timetables.

Greetings
You should be able to reserve almost any train ticket in the UK via http://www.nationalrail.co.uk/times_fares/. You do the search for train times there and then can pick which website to book on - you can book any train with any company, but companies usually offer the best deal on their own tickets. And there's no booking charge. It looks like you can book your tickets - not cheap as it requires at least two changes of train, but certainly doable.

You will need to use a UK post code for the ticket booking - use the one for your hotel or accommodations and then switch it to your US one for payment address. Tickets are not sent abroad, but you can print them out from the machine in London.

Kate

If you have cheap long-distance phone service, call British Rail during their "normal working hours". They can make reservations, and you can make specific requests, such as the "quiet car", which is a no cell phones, no radios, etc. car that lets you watch the scenery, read, or quietly converse.

I have bought tickets on-line, and picked them up at the stations in the UK. But since they, and you, are English speaking, it sometimes makes sense to just make a phone call.