Train journey sounds about right, there isn't a direct train from LHR to Worthing.
You could possibly consider flying into London Gatwick (LGW) rather than Heathrow it's much closer, trains to Worthing take about 45 - 60 mins.
Coach travel is another option but it's very slow, 4 hours direct to Worthing from Heathrow. You can however get a fast Airport link Coach between London Heathrow and London Gatwick, they leave several times an hour and takes about 75 minutes then take the train from there. More details on national express coaches here:
Best bet for Stonehenge is to get a Train to Salisbury and get on the hop-on hop-off Stonehenge tour, it departs hourly in the summer. More details here: