Offtopic much?
Since OP is planning to visit for around a month, I would imagine that being near to an airport is probably not important and that he'll be travelling around at least a little.
Can't speak for best spotting places, but as I'm sure you know it's passenger rather than freight which dominates UK rail - coming from the US you'll probably not be very impressed by our tiddly freight trains! Most passenger trains are multiple unit rather than locomotive hauled. I'd say somewhere on the
WCML for a mix of fast passenger (
390,
221), regional (
350,
220/
221) and freight (mostly diesel hauled with EMD Class
66, though a few GE
70s and a bit of electric (
86,
90,
92).
You could visit Didcot on the
GWML (taking in Oxford too for non-rail tourism purposes) where you'll get more freight (66s), the odd bit of shunting (switching?) in the adjacent goods yard, along with some vintage action from
Didcot Railway Centre with a collection spanning the mid-19th century to the 1980's, and from
HSTs, which pass at full speed.
Most of the London stations are worth a look in, with plenty of traffic and some nice architecture - I'd recommend Paddington, Kings Cross, St Pancras (beautiful station but awful to use) and Waterloo. Clapham Junction is also quite impressive just in terms of number of trains!
In terms of lines to travel, I'd recommend the usual suspects of Settle-Carlisle & West Highland, though you'll not see that much rail traffic on these. I find the WCML London-Glasgow interesting in terms of the variety of landscapes, towns and railway sights on the 4h30 journey (make sure you get a seat with a window though!). The line from Exeter to Penzance is also very nice.
If you do plan to travel much by rail, bear in mind that there are various products available to tourists which are much cheaper than can be obtained within the UK - you have to purchase these before arriving. Even if you just plan the odd trip you may be able to save some money - try our Fares forum if you're interested, and bear in mind that for long distance journeys it can be (but isn't always) worth booking in advance.