Silkspan expands when wet, then dries to the same size it was before. The one time I put it on dry no amount of tautening dope would tighten it. Every time I've put it on damp it's dried to the perfect tautness.
Different brands may act differently -- my only experience is with Sig. Doctor paper may act differently, too.
Tissue definitely shrinks. It should only go on damp or wet if you're covering a compound curve. For outdoor rubber powered planes I like to shrink it by wiping it down with a cotton ball that's been wetted with 70% isopropyl alcohol. That makes for a nice even application of just the right amount of water when the alcohol flashes off. For indoor rubber or really small outdoor planes you shrink the tissue on a frame, then cut it off, crumple it a bit, then put it on the plane. Otherwise your plane will potato-chip as the tissue shrinks.
I think I'd only use tissue on 1/2-A planes, and then I may use it double-thickness. If you go out and buy it, stick to Esaki -- all the other stuff I've bought recently has been crap.