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Subsonic said.. >>> generally you'll need to wet out the surface with resin then wet out the fibreglass as well to ensure good adhesion. Then use peel ply cloth (ask about it at the shop) or something similar to remove excess resin and create a flat surface that won't require too much sanding.
good luck
Agree with the previous Subsonic, but if I was doing it, I'd only work on horizontal surfaces for a start, it's much easier to control where the resin goes and gravity helps you soaking out the cloth. Unless vacuum bagging I wouldn't use peelply. Just squeegee out any excess resin, (buy a squeegee), overlap layers by around 2cm. when all surfaces are covered a layer of filler coat, then sand smooth.
If using polyester resin, use laminating to wet out the cloth and filler as the final coat. You can't sand laminating resin, the surface never quite sets, so you get a good bond with the next layer.
I'd use plain weave cloth, not mat. Unless you want a thick layer of glass. 9mm marine ply should give all the stiffness you need, possibly 1 layer of 125gm cloth is all you'll need, but as subsonic says talk to the person at the counter about strength abrasion resistance requirements.
The other thing with glassing over timber, is the shrinkage/expansion differences between timber and resin/fibreglass. I think most of the problems are more due to moisture than heat. It would probably pay to completely seal the timber, so the moisture content doesn't change after you glass it.
EDIT, just had a quick look at your plan, important thing to keep in mind, fibreglass doesn't like hard bends, it will pull away from one or both faces and form a curve, so you'll get a void. It's better to round off all corners. A 2mm radius is probably enough, unless the cloth you use is very stiff, again ask the assistant.