Getting to Stonehenge - any company better than others?

When you say "in the morning," do you mean access to the inner circle before the henge opens to the general public? Or just a visit during normal open hours when the inner circle is roped off? We did the former on our own (booked through English Heritage, had a rental car and drove from Newbury at 4:30 AM), but if I went again I would like to try the tour by Pat Shelley. http://www.stonehenge-tours.com/

Ideally the early morning with inner circle but the only day I can visit is September 20. The sites I've checked are sold out or don't offer that day.

Yes, September 20 is just 2 days before the autumnal equinox, so that date is probably attracting many more visitors than usual.
If the early morning time slot for "stone circle access" simply isn't possible, I'd suggest booking a regular opening hours timed ticket ASAP. https://bookings.english-heritage.org.uk/stonehenge/sessions.aspx?tid=2

If you're like me, you'll thoroughly enjoy Stonehenge even from behind the ropes. There's an excellent audio guide (wear around your neck) and the visitor centre is full of fascinating exhibits, indoors and out. It also has a well-stocked gift shop and cafeteria. You take a short shuttle bus ride from the visitor centre to the henge, or you can walk all the way, or get off halfway. You can also walk a greater distance to/from Woodhenge and Durrington Walls, about a mile to the east. There is plenty to see, so don't feel you are missing out by not getting stone circle access.

I did find one for 16 September with inner circle. Its not an actual "sun rise" tour, but we still get there pretty darn early. Pat was sold out.. bummer! So I rearranged my schedule and now its Saturday the 16

I know that if I did not get inner circle my life would not be ruined, but having traveled so far, it would be nice if I did get it.
I got a spot with Evan Evans Tour at $160 pp, so I'm good to go.