I am trying to work out if it is worthwhile me getting a rail pass and am checking prices for journeys on HyperDia. This says that a 'fare' from Tokyo to Kyoto for instance is 8210 yen. But then there is an additional cost listed of 4870 for a seat (or 5700 for a reserved seat). So is it the case that the 'fare' price is never the actual price paid and that the additional cost of a seat always has to be included?
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The actual fare is the base fare + the seat fee. Both are mandatory. So for going from Tokyo to Kyoto for example, or vice versa, it is ¥8210+¥ 5700 which comes to ¥13910. If you want it cheaper, then going with an unreserved seat which is ¥4870 makes it ¥13080. Since you can almost always get a seat somewhere (except perhaps during a peak season), the ¥13080 should be the amount you use to calculate if it is worth it to get the rail pass.
You could also go by a Green Seat which is nicer and more expensive if you wish. For the rail pass, advance seat selections are a free perk thrown in, but they are not necessary - with the exception of a few trains like the Hayabusa bullet train which requires advance seat selections.