I agree with Lofty, except with 15 mm thick ply, I would use a No. 5 or even a No. 7! This highlights a "problem" with fret sawing (machine or hand) - "what suits Joe may not suit Tom"!
But they're cheap enough that you could afford to buy a dozen of each - personally I like Pegas and Axi are the UK distributors. Niqa and Olson are also good, but I THINK you have to get Olson by post from the US. Niqa are - I THINK - sold by Hegner who also are in UK. Hobbies in Norfolk (mail order) are also a source and again I THINK their blades are Niqa.
Reverse tooth blades have the first few teeth (at the bottom) pointing upwards, the idea being that when cutting thin or splintery stock, it reduces any splintering at the bottom of the cut. Skip tooth blades have, as the name suggests, every other tooth (or so) missed out, the idea being that when cutting thick stock there is more space in the kerf to clear saw dust. Spiral blades have the teeth all the way round (the blade is actually wrapped into a spiral during manufacture) and as you said already, will cut in all directions. IMO you don't need those. I find them very difficult to use anyway, but that's just me - some swear by 'em!
If faced with your job, I'd order 3 packets of a dozen blades each from Axi, ordering the Pegas "MGT" (modified geometry teeth) bIades in sizes 3, 5 and 7. A dozen of each should be more than enough to do the job with loads left over, and they're cheap enough for what they are.
HTH