Rather than travel to central London to take the train, consider using the RailAir coach to Reading and joining the train there. The journey from Reading to Birmingham New Street takes about an hour and 40 minutes, with no change of train required.
You can check times and fares and book at www.nationalexpresseastcoast.com - if you want to go back to central London after your stay in Birmingham, you'll need to book two singles rather than a return, but they may be cheaper in any event than booking a return from London.
With five terminal buildings at LHR time of day and day of the week can make a difference in the time it takes to go through passport control and collect bags. You'll need to allow a bit of time to get from Arrivals to the Central Bus Station, again depending on the terminal at which you arrive.
Sadly, Heathrow is one of the worst major airport in Europe for public transport links. Almost all train services require a change in London. Not only is this staggeringly inconvenient, it also means that your trip to Birmingham starts by going in almost exactly the opposite direction to the one you want to travel!
Trains to Birmingham actually go from both Euston (Virgin) and Marylebone (Chiltern) though the latter is a slow stopping service.
For ease, though, I would probably opt for the bus. It takes no longer, involves no changes, guarantees you a seat and could calso prove cheaper.
Your flight with US will actually arrive from PHL, so I hope you've allowed enough time to change planes at Philadelphia. The flight will arrive at LHR Terminal 1.
22 May is the start of the late May Bank Holiday weekend, with half term for a number of schools the following week. I think you may be wise to book tickets for the coach before the day of travel, just to ensure you get seats and to have one less thing to do at Heathrow.
From T1, you'll take the lift down from Arrivals as if you were going to the Underground station. Instead, walk towards Terminal 3, following the signs for the Central Bus Station. There are travelators in place to help ease the journey, but the walk shouldn't take more than ten minutes.
There is a coach departing from the CBS at 1300, and with an arrival time scheduled for 1105 you should be able to make that departure. If you'd rather have a bit of time to allow for delays in passport control, baggage collection or even for US to get the plane to the stand on time, then the 1415 departure should be suitable. www.nationalexpress.com for booking info.
Since friends will be picking us up in Birmingham, would Birmingham Int. Airport or Digbeth Central Coach Sation be better for the pick up as far as parking or if we are late etc.?? Also, I have the coach route but am not sure if we stay on the same coach the entire journey or do have to change? You have been so helpful!