the brackets have a hole at the end so you can screw vertically into the board to stop it wobbling or slipping out of place. But this is not strong. If you have an overhang, and try to climb up it, the boards will tip up and plummet to the ground with you.
I would hesitate to have an overhang of more than 50mm. No overhang at all if you have climbing urchins.
btw you say cut them with a jigsaw. A jigsaw is suitable for cutting complex shapes. It is not suitable for cutting a square straight edge.
If you have not bought them yet, some DIY sheds will cut to size for you.
Otherwise you can do it with a panel saw. Even a cheap one will not go blunt before you have cut your shelves.
18mm ply is very strong, and will carry, say, a microwave or a shelf of books (which are very heavy). Thinner board will tend to bend in the middle. You can get "hardwood faced ply" which has a decorative veneer on at least one face, suitable for staining and varnishing if you wish. The cheaper grades are increasingly likely to have dead knots and cracks in the surface, as they are made with cheaper veneers.
If you want an ornamental front edge you can glue on 18mm stripwood, with a few pins to hold it while the glue sets.
Ply and other sheet materials are usually sold in 1200x2400mm boards, sometimes 600x2400 or smaller fractions. You will find it difficult to carry a full size board. Try to calculate your sizes with the minimum number of cuts, as you may be charged per cut.
BTW I would use brown plasplugs, not red, about 30mm long, and tap them slightly below the surface of the plaster, which will reduce risk of cracking. The flat piece on the block of plugs is engraved and has holes for the drill size and screw sizes that fit.