Unfortunately, I don't think looking at average fares will be helpful in this situation. Great Britain has about the widest-ranging fares I've seen. What you will pay for a non-refundable/non-changeable ticket at the promotional price far in advance can be a small fraction of what you will pay if you buy the same ticket on the day of travel. To determine whether the Britrail pass is a smart purchase for you, you need to decide whether you would otherwise be ready to buy some or all of those tickets quite soon, or whether it's worth the extra money to you to maintain total flexibility and pay day-of prices.
The best source for fares is the National Rail website. For the maximum you will pay, check for tickets for the current date. It's probably too late to do that today, but you can take a look tomorrow morning. What you can do today is check the fares for the likeliest dates for your trips. I took a quick look at fares for around 8 AM on Friday, June 8.
Dates can matter a lot, as can time of day. Trains during commuting hours sometimes are quite a bit more expensive than those at off-hours, but these are fairly long day-trips, so I assume you will want to get an early start. As for the dates, Thursday and Saturday might be less expensive than Friday. It will be worthwhile for you to figure out what is likely to be the most expensive trip if you buy tickets late, and explore all the possible travel dates to choose the least costly one.
Finally, fares can vary by rail company/route, and those are linked to the departure rail station in London (of which there are many). If you have a preference for a particular station, that's something to consider while you're doing your research.
All fares are roundtrip and per person.
Warwick: £11 (Marylebone)
Portsmouth: £24.40 (Waterloo--looks cheaper--or Victoria)
Stratford-upon-Avon (use full name): £14 (Marylebone--looks cheaper--or Euston)
Canterbury: £34.10 (Victoria or Charing Cross, or the more expensive St. Pancras)
The Canterbury fare is an "Anytime" fare that--as I understand it--doesn't lock you to a specific train. I believe you can walk up and buy that type of ticket the day you want to travel; I hope someone else can confirm that.
As you can see, if you're willing to buy the first three tickets soon, you probably have nothing to gain from a BritRail pass.