What's the most slippery thing I can polish wood with?

Why not polish the for sale sign and see how it goes? if it works, order some, if it doesn't work you will have a very clean and shiney for sale sign

 

I have just taken a walk across our kitchen floor, and instantly thought "lino flooring"

You should be able to get an off cut from your local carpet shop, lay it over the top of the ply, then polish it up.

 

That's genius. Sounds like a plan. And the best bit is if it works, it will fit in with my mission to build the thing on a tight budget. I would have had no problem spending around £60 on a plastic sheet, but it would have felt like I'd failed in a way, as so far the entire thing has only cost me about £20 in materials, and most of that is nails, screws and bolts. I got a bit short of wood so had to buy some, but the bits I bought were off-cuts (3 of 4"x3"x about 4ft posts - £1.50 each, and the two plywood sheets at £2.80 each).

 

Personally I wouldn't 'paint' the slide with anything. If you want a truly durable finish begin by smoothing off the surface with a fairly coarse wire wool, and keep sanding with finer and finer grades (raising the grain between each sanding) until you're down to 0000 by which time the surface will be like glass, then you can protect it by rubbing in something like Danish Oil - you only use a tiny amount which is absorbed into the grain so we're not talking oil-slicks or oily trousers here. Do both sides (of course) and the rain will run off, the wood will be protected and all you have to do each year, is give it another rub over with the oil.