I assume that 'we' means two people- so buy a Two Together Railcard for £30. That is only valid for journeys starting any time after 9.30am on a weekday (anytime weekends).
All prices below are for 2 people with railcard,
Journey a- You can't predict what time you will land. So buy anytime Day Singles £63.90. Your origin point is Heathrow Terminal [x] Bus, with x being your arriving terminal. A complication has been found this week with such tickets. They can not be issued as e-tickets, only as physical tickets. The bus leaves from arrivals at each terminal, but you will have to collect your ticket first from the machines at each terminal's rail station, then go to the bus stop.
Journey b- The 0947 is the 1st train you can use, arrive Axminster at 1104. Go upstairs on the bus for the best views. The bus costs £2 each each way.
For the train either buy a Semi Flex Return for £41.80. Or, if you are willing to be tied to specific trains-
the OUT journey is £15 and the BACK journey is £10.40. Your choice
Journey c- £45.20 Any Time Single if you want to be flexible, or an advance fare if you are willing to be tied to a specific train. On the 0947 that would typically be £21.20, wait until 1247, 1347, 1447 or 1547 trains and it will be as low as £9.30 for the two of you.
Journey d-
Buy in 2 parts-
Woking to Waterloo £19.10 Anytime Day Single (on the 33 minutes past the hour train, arrive at 17 minutes past the next hour)
Waterloo East to Canterbury £17 Advance Fare (on the 37 minutes past the hour direct train)
Journey e-
Canterbury to London Waterloo-
Travel at or after 1107 on the 7 minutes past the hour train- Advance Fares £15.10
Canterbury to London Victoria-
Travel at or after 1947 on the 47 minutes past the hour train- Advance Fares £15.10
Canterbury to St Pancras-
Travel at or after 1123 on the 23 minutes past the hour train- Advance Fares from £18.80, vary by train
At these fares a Britrail Pass won't pay. If for every journey you want full flexibility with times you come and go then it undoubtedly will- the London Plus pass I think it's called. NOTE- That is not valid on the Heathrow to Woking Bus, it is also not valid to Axminster.
You are travelling on multiple train companies, each of which can issue anyone else's tickets. The best websites for a visitor, by far, are LNER and Northern Rail. Most people use LNER.