So here are some things to consider. I'm not suggesting any other way or materials would not work out but here is what I have found out over the years of older fiberglass boat retorations.
Epoxy resin is a better material when it comes to strength AND adhesion. It is also less permiable when it comes to water. Also, I like it because it does not smell when you are using it. It is compatible with foams and wood etc.
DO NOT USE chopped glass mat with Epoxy!!! The chopped glass strands are held together with a light bonding agent which disolves in polyester resin but not epoxy!!! This will result in very poor wetting and strength if using epoxy. The exception to this is there is a Biaxial stitched cloth that has a layer of chopped glass with it, the bonding agents are not used when making this laminated cloth. It is the glass fibers that give the strength to a boat and if not well bonded down they cannot impart this strength ot the hull.
As far as cloth types go stitched Biaxial is the best for stiffness in all directions for a given weight. Weight per square foot of material is how cloth is measured rather than thickness. Because of the many weaves that can be done, thickness is not a good measurement of strength. It's the amount of glass fiber per square foot so the industry uses weight. A layer of chopped glass and biaxial might be the same thickness but the biaxial will have more fibers so it's be heavier, it will also be stronger both because of the fiber count and the orientation of the fibers.
www.fiberglast.com has a neat sample pack of different weaves and weights to help selecting what is right. This material is not woven so the fibers lay flat on each other, this makes it stronger becasue the fibers are straight and not weaving up and down over each other. The typical 90 degree cloth weave is inherintly not as strong, plus as the fiber count is increased the weave gets coarse, then being called woven roving, leaving more space for resin which adds weight without adding any strength. Roving is strong because there are so many glass fibers but, it is heavy. Biaxial tape is best for stringer bonding if you think about it all the fibers will be bonded to both the stringer and the bottom, crisscrossing across the joint, where as a 90 degree weave tape will only have the fibers in the width direction bonded to both the stringer and bottom, across the joint the lengthwise fibers do nothing to reinforce this joint as they run parraleel to it not across it. The Biaxial goes into a corner much better as the fibers are not bending as much because they are on a bias, wheras 90 tape the fibers have to bend at a 90 degree sharp corner. You should fillet inside corners with thickened resin and round off outside corners by grinding so the glass does not pucker leaving a void underneath, very little strength if that happens. I use the 90 degree cloth just to protect plywood faces from abrasion and water. You can get vey light weaves for this purpose so not much weight is added.
When doing a balsa core I get the biaxial with the chopped layer stitched on. this gives the good resin rich layer to bond to the balsa, the chopped side, with he strength of the biaxial. This material is compatible with the epoxy becasue the bonding agent is not used to hold the chopped layer together, it's the stitching that does. Everywhere else I use plain Biaxial cloth and biaxial tape. I use varying weights depending on what is being held together or reinforced.
Chopped glass is the least desireable strength wise, it's also likely to hold more resin by it's nature when laminated by hand, therefore will most likely wind up being heavier. Keep in mind the manufacturers use different techniques than hand laminating and cost is a consideration. Biaxial is superior but it is more $$$$.
Polyester resins do not have as good of adhesion to CURED polyester resin, it sounds illogical but, this is true. Almost all production fiberglass boats are made with polyester based resins. Where we are adding stuff back onto a bare hull adhesion is important. Down side of epoxy is the blush, which is a water soluable wax like residue that appers during curing on the top surface, this needs to be washed off (use water and soap NOT a solvent) and then the surface light sanded before further laminating or bonding can be done on top of fresh cured epoxy work. It is extra effort in this regard but I feel well worth the time. You cannot use gelcoat or plyester materials on top of epoxy, this is bad chemistry. Again may sound wierd you can use epoxy on cured polyester but not polyester on top of cured epoxy. Strange but true. Epoxy does fine with primers and paints. I use Imron or similar catalized urethanes for my finishes, no problems, looks great, it's hard and glossy although not as thick as gelcoat. It stands up fine in my experience.
Marine plywood is vastly superior to exterior grade plywoods due to better core lamination quality and more plys are used. This makes the panels stiffer and with no voids for weak spots. I use Okume species Marine ply becsue of it's strength yet lighter weight than Fir, Mahogany, Sapele or other speices. I am luck a local supplier has it readily available. Search on Boulter Plywood, Somerville MA, if you want to read about the differences in plywoods available, they list weights of the materials too. Very informative. Okume is great to bond too also.
Plywood edges are the bug-a-boo as it will readily wick water if not sealed. I use solid wood for stringers for this reason. It's only the small endgrain area that will wick water if not sealed not the top grain on the four sides so it is easy to insure they are protected.
Balsa from an impact point of view is vastly superior to foam, it is easy to handle and has terrific bonding strength, the resin penetrates well. The panels that are used are flexible to conform the the curves of the bottom because they are panels of 2x2 squares held together with a scrim cloth. Down side is it's wood. It has to be sealed, this is not hard to do, any drill holes put in later must also be well sealed. Again, Epoxy is superior for installation because it is a better water barrier. Believe it or not polyester will absorb water this is measured by permiability. This is why any good marine survey will include a moisture reading of the fiberglass hull. Read the WEST epoxy website, they have comparisons for epoxy vs polyester in this regard. Very interesting and not intuitive that water does get into what appears to be a solid material used extensively for boat building.
Clarify? Confuse? Most likely what ever you do will be fine, certainly better than the rotted stuff you removed. Cost is always a consideration but I balance that against the time I put in and of never having to do it again!
Good luck,
Randy