Hey JDR,
You didn't mention how long you'd be staying or how much luggage you'll be hauling?
Well, either way the Heathrow express may be a teeny-tiny bit more comfortable when hauling luggage but is not worth the expense, particularly as it isn't very convenient to your destination. Though the Tube can take up to about an hour at times to get into central London it's mostly above ground all the way and will give you that first "We're not in Kansas anymore" feeling!

) It's a wonderful mix of beat up areas and funky back gardens. On arrival do not wave your camera about too much and please watch your bum bags (fanny packs?) and wallets while on this line into London and at the stations on your arrival when you'll be tired, off guard and particularly looking like tourists. I'm sure you're a well seasoned traveller but London does have some of the lightest fingers on the planet. Once your just one of the masses though you'll probably be in one of the safest, cleanest and most beautiful cities on earth.
So with this and the other opinions posted here consider that question sorted - Tube it is!
2: The London pass is really, expensive, but it entirely depends on what you want to do and how much time you have. London is incredibly overwhelming - you can easily walk around and be slack-jawed by the sights all day for days. Some of the tourist attractions are decidedly underwhelming once inside, particularly considering the amount of time you spend queuing and the expense. For example the London eye is an engineering marvel, but a trip around in it is pretty boring actually and the view through the glass and through the often murky London air is nowhere near the Picturesqueness(?)of the view from the Greenwich park. The Tate modern is amazing, even for non artys, in fact all London museum's are among the best in the world with many hands-on exhibits. Best of all is that there's a tube station right next to every major attraction. I have in the past brought "done" London in just one day whenever showing friends around. Lastly on this, don't go on one of those open top buses - you'll end up stuck in traffic, listening to a largely incomprehensible tour guide shouting in your ear.
Oh,i'm just thinking of the very unfavourable exchange rate. Yikes! Have you booked a hotel yet? - that's another potential minefield!
Cotswolds? - Yeah, yeah, yeah!

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Great that you're not just going to be stuck in just one place. Oxford, Windsor, bath are pretty, Stonehenge is impressive, (I prefer Avesbury for pure scale) but these are reasonably large places needing some time to explore properly. Consider then taking the train to a larger town just outside the London urban area or in the Cotswolds that offers car rental. Car rental can be so cheap, particularly in rural areas. Though you'd be insane to rent in London a car, besides a bicycle, is the best way to see the winding country lanes, lakes, countryside and, of course, very close to my heart the many local pubs, tea-houses and cake shops. There is nothing quite like the cotswolds anywhere on earth and it's both a wonderful contrast to London and so stereotypically English you'll have a Griswald moment there.
As for photography, Hah! In London you will turn a corner and seee something new worth taking MANY photos of, then the next day, because of the changeable wether, you'll see the same thing again in new light and take the same photos again, only better. London was the capital of a huge Empire and they used all this plunder to build one of the most ostentatious displays of imperialism in the world. all those classical images of London? wait till they're within your viewfinder. Just don't forget you have a wife and children there with you!
Eh, hope I was of some help!

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