Came back through Heathrow T3 yesterday from the US. There are two train options, travel via London or take the Reading link bus to Reading and catch the Cross Country service to Manchester which stops at Stafford. The Reading route is longer by an hour but if you have lots of luggage it might be easier as the bus stops outside the Station and it's and a short walk to the Platform. Going via London, the cheapest way is the Tube from T3 or T5 on the underground for £6 to Kings Cross and then a short 10min walk down Euston Road. The alternative is the Heathrow Express to Paddington station, bought in advance by a few days it's £22 and is the quickest route, a taxi black cab from Paddington to Euston station is £13 and takes 5-10mins depending on traffic. The advantage of the black cab is that they use the bus lanes which speeds up the journey. There is a bus and tube alternative between the stations but I've never used it. Euston to Stafford: two train services are the faster Avanti or slower Midland trains. Tickets can be bought online via Trainline.com. After a redeye flight over 6-10 hours I would take the more comfortable Avanti with tickets and seats bought in advance. There is National bus services but it takes ages and the nearest and most frequent stop is in Penkridge, only used it once and never again.
Yesterday I went via the Paddington station route and it took 2.5 hrs which was slightly less than waiting in the immigration queue. If you're travelling soon I would be careful about booking tight connections due to delays at immigration.
If flying to Manchester catch a taxi to Stockport £20 and then take the train directly to Stafford. There is a train from Manchester Airport station to Stafford but you need to change at crewe and it's not as frequent to the Stockport - Stafford service.
There are some flights to the US you can still catch if you catch the first train to Euston and grab a taxi to Paddington Station and then the Heathrow express. for a checkin at 9am.