Glad it arrived safely - quicker than I expected as well
It's annoying that the 7815 and 7915 have different pin-outs (the input and ground terminals are swapped). The 7815 has the nicely logical pinout of IN, GND, OUT, as viewed from left to right on the PCB. When it comes to the 79xx series, I always look them up to double-check. Once upon a time I had it locked in memory, but since getting ADSL at home, I'm getting lazy...
It's a clever little PCB - someone really thought that through. For the 78xx, you populate the components on the right, and the opposite is true for the 79xx. Of course, the 4700uF and bridge rectifier are needed in either case, along with the 470n in the middle (those caps aren't critical, BTW - anything between 100n and 1uF would be fine there). Note also that the connections at the bottom change according to the regulator fitted.
It's worth saying - and I hope this helps - that how to use that board might be obvious to some of us on here, but that's only because we've been using the chips for years, and know how to pander to their needs. But without the explicit instructions from RS, it's definitely confusing for someone who is relatively new to all this!
If it helps, you don't need to use such a large smoothing capacitor. 4700uF is massive. For your oscillator PCB, for example, you could get away with a tenth of that value. To determine the appropriate value, you could go through a whole load of maths, or you could follow rules of thumb or similar. In other words, it won't hurt to experiment a bit. The value has an effect on ripple and stuff, and by implication, how low the mains needs to dip before 100Hz ripple appears on the output (try that on your variac!). But do watch the voltage rating. Take the transformer voltage (say, 15V), add 20% to that, then multiply it by 1.4. That's very close to 25V, and a 25V cap would probably be OK, but it wouldn't hurt to go for 35V. Verify it once built by ramping your variac up to 250V or thereabouts.
Another thought - probably more of a "thought experiment" at this stage - is that you could build both boards identically. That's right - you can make two identical 15V supplies using 7815s, or even 7915 if that's what you have to hand*. Having done that, recall a point I made earlier - because both boards are producing 15 volts that is floating - both with respect to earth, and with respect to each other - then you can think of them as being batteries. So you can connect them in series to make -15, 0, +15.
(* Yes, I know you've got samples of both regulator types on their way, but it's still a useful concept to chew over during a quiet moment. In practice, it is sometime done because negative regulators don't always behave as perfect mirror images of their positive counterparts.)
Anyway, glad you're sorted for this project - and the next**
(** Hmm. A simple TDA2030 amplifier to "beef up" the output of the oscillator board is worth thinking about. And RS used to make a PCB for that IC: 434-576, it seems. I don't have any here, but I'm sure someone on the forum could come up trumps? Sorry - I'll shut up now!)
All the best,