You guys are great with many timely suggestions.  The key to my failure to find the Group 4 savings was identified by devonian, and agreed to by John R - it doesn't compute with RailAir.  When I tried again using both Heatrow rail-NTA^» (Newton Abbott - next trains) and RDG^‡(resolve)-NTA it worked fine.  Therefore, as advised, using Group tickets sounds much better considering restrictions for Advance.
Based on the comments, I would feel more comfortable in recommending the connection in Paddington then before, and, as mentioned, the advance fare is a good option for those originating travel from Paddington.
The largest portion of my group will be arriving at Terminal 5 on the British Air non-stop from Atlanta, and it looks like RailAir has a discounted ticket for a group of 8+ to Reading, which combined with the Group 4 or 3 savings from RDG-NTA will result in the best alternative.  Another sub-group of at least 4, including myself will be flying in on Delta at Terminal 4, but we will be arriving earlier and I feel confident in navigating Heathrow to the Central Bus Station to catch the RailAir.  Hearing that it is easy to get from the RailAir to Track 4 in Reading is reassuring.
And I will certainly advise my group to sit on the left side of the train for the scenery.
Thanks so much for everyone's input, and I will try to stop by the Coffeeshop periodically to see what's happening.

Thanks to all who responded for your thoughtful comments on this.  Based on the comments, things look good for the magnetic stripped cards.

An issue which is getting more and more attention in the US is the fact no US banks are issuing the type of credit card with the chip and pin that is in use in Europe.  Sadly, all of our credit cards have only the magnetic strip.  I have run into two situations during European travels, thus far, where I could not use my credit card, once at a fast food restaurant in Richmond, and the other to purchase train tickets in Barcelona.

I have been told by a GFW customer service person that it would be no problem to buy tickets on line and then pick them up using my credit card once I arrive from overseas.  He stated unequivocally that all the machines will accept the magnetic strip card.  Experience has told me that it is good to verify such critical information, so that is what I am asking.  Thanks, again.

As I posted on the "introduce yourself" page, I am the trip coordinator for a group of 33 Americans who will be arriving in May for a week's walking around Dartmoor - South Devon. 

I am trying to figure out what advice to offer my group regarding the purchase of tickets.  I have spent considerable time on both the Nat Rail and FGW^▸ (First Great Western) websites, so I am pretty familiar with the schedules, etc.  Part of my questions relates to applying what I have learned.  Here are the group particulars:
Each person is booking his own air, so everyone is not arriving the same day or on the same flight.
- However, we will all be traveling to Newton Abbot on Saturday, May 8, and we will all be leaving Newton Abbot on Saturday, May 15. 
- Not everyone has booked their flights yet, but as of now, all will be traveling to Newton Abbot from Heathrow except for a few early arrivals traveling from Paddington.
- I am planning to advise the use of the RailAir coaches to Reading and then connect to the train, as I think this will be less stressful than connecting in Paddington, and hopefully less expensive.
- Due to the timing of flights to Heathrow, I know that we will have a group of over 10 traveling together, and also one or more groups of at least 4, but less than 10, traveling together.
- Some are planning to fly from Exeter to other European destinations, so they will not be requiring a return ticket.

So what is the best option for the best fares.
1.  Advance tickets?  When I checked yesterday, the fare for midday Heathrow-NTA^» (Newton Abbott - next trains) one way was 57.5GBP and the return with a morning departure was 115.  Am I correct in assuming that anytime on Saturdays is considered off-peak?  I know that advance tickets pertain to a specific train which can be a bit problematic after an overseas flight, but I am advising a two hour interval between scheduled landing and airport departure.
2. Groups of 10 or more travelling together?  The GFW webite indicates a 26% discount.  But what is the base for the discount?  Can it be combined with the advance ticket savings?  If not, which is better?
3. GroupSave for 3 or 4 people travelling together?  OK, 3 or 4 can travel for the price of 2 adults, but again, what is the base for the discount?  The GFW website says that this fare can be booked on line, but when I tried to find the price for 4 people online, even after using the dropdown box for the group discount, I got the 4 times the price that I listed above.

As you can see, I am a bit confused and overwhelmed as to what is the best fare.  Any help and suggestions on this would be most welcome.  Thanks!

My name is Bob and this is my first day as a registered member.  I live in the USA near Atlanta.  I am retired and major interests are world travel and walking.  I have had the pleasure of meeting many Brits through these interests.  I have spent 5 weeks over several years walking with Brits through a company called HF Holidays which some of you may know.  My wife and I have also traveled 3 times with the UK^▸ (United Kingdom) company, Explore (to Romania, Portugal, and the Baltic Republics).

This brings me to my reason for registering.  I am the trip coordinator for a group of 33 Americans who are coming to England in May for another week of hiking with HF Holidays in Dartmoor - South Devon.  I have some questions regarding how to arrange and pay for the group's rail travel to Newton Abbot.  I will be posting these, hopefully, under the correct topic.

I am looking forward to visiting your country again, as I am an admitted Anglophile, and will appreciate any helpful suggestions.