"How should we get from LHR to the hotel and back?"

Can't help w/ that w/o knowing which hotel-

"Where should we stay?"

Can't help w/ that w/o knowing your budget-

"one day in London seeing the tourist stuff you always see in movies (big Ben, eye of London, bridges, double decker bus, bucking ham palace, changing of the guard, etc)"

You can't visit even a fraction of the main sights in one day. There are Hop-on-Hop-off tour buses that will let you ride past many of the sites, but you wouldn't have time for more that that and maybe one major site - the Tower of London or Westminster Abbey or something else. The main problem w/ the changing of the guard is it eats up a LOT of time. You need to arrive about an hour ahead of time if you hope see anything -and can't leave til its over.

If you must go to Stonehenge, then I would just pick a couple of the main sites and see them on your free day in London. The Tower of London would be THE 'must' for most first timers. The Tower and the Eye plus a river cruise - or Westminster Abbey and the Tower, something like that. Big Ben/Parliament/Buckingham Palace are just 'walk-by's' so you can see them too (avoiding the Palace during the Guard Change)

For Stonehenge, get the train from Waterloo to Salisbury and the bus from there.

At Stonehenge, work is going on to develop a better access experience than the existing utilitarian entrance and carpark. You don't say when you'll be there, but don't be put off by that. Try to allow some time to walk further away from the stones so that you can see them in the context of the wider landscape. Go down the slope along what they think was the ceremonial approach avenue, and then climb back up towards the stones; take a look at some of the burial mounds ringing the site; if you can, cross the main road and go up the slope the other side to see how the stones just seem to disappear into the landscape.
http://www.thestonehengetour.info
http://www.english-heritage.org.uk/daysout/properties/stonehenge/

Not being funny, but with only two days in London, Stonehenge is a long way to go to see a pile of rocks.

Really, I can't see what the fuss is about. Stay in London, there is SO MUCH to see. Your description of one day seems to be a series of flybys without actually going inside and seeing anything.

We will be there in late March.

Agree with skipping Stonehenge. There is too much to see and do in London without spending an entire day to and from Stonehenge.

One of my favorite time-savers is seeing the Horse Guard Ceremony instead of the Changing of the Guard at Buckingham. We usually get off the Tube near Big Ben, walk around Westminster and past Houses of Parliment, through the park to get a peek at Buckingham, then head in the opposite direction of the crowds to see the Horse Guard ceremony.

Save the Eye for later in the evening, once everything else is closed. Reserve ahead of time.

Tower of London is my must-do when I take vistors to London.

The hop-on-hop-off double decker bus tour is perfect, especially if it is your first visit. I recommend getting your tickets on line (always cheaper). When you purchase on-line you always have the option of adding other attractions. I highly recommend the 'walking tour'. It is very entertaining and includes an unknown by many view of the 'changing of the guards'. This begins at St. James Palace. (not the walk). You can do the walk in the morning and then get on the bus to tour the city.
I also recommend you stay in London to tour properly as you only have 2 days. In order to take a bus to Stonehenge it will take up almost 1 whole day. As visually interesting it is I do not want you to be disappointed. It is in the middle of no where and can be easily done if you were to have a car and were driving to Bath (Devon & Somerset) on your next visit, for example.
I agree, The Tower of London is a must. With the hop-on-hop-off bus tour it also includes the river boat cruise. I recommend getting off at The Tower! Do a tour inside, then take the river boat cruise (pick up right at The Tower) and travel down to Big Ben and The Eye.
Enjoy!