First off, working with plywood needs to consider more factors than working with 100% mill type lumber woods. While milled woods are solid, plywoods i ncorperate resins or glues to adhear and sandwicht them as to hold them tog ether. In plywoods, most resin/glues are "somewhat" water proof when cured but only if exposed to moisture for a short period of time, but will eventu ally break down as the duration increases. This is because wood swells when it absorbs moisture then contracts as the wood re-dries, thus causing the resin/glues to release/crack/split... forgive my over detailed captin-obvio us here.
Natural Resins are in the tree (the in the form of saps) which will help se al and hold wood long fibers together so lets just keep that in the back of our minds for a little while.
Plywoods are also made from thin layers of woods that go in several directi ons (for strenght applications) plus the adheasion layers (as mentioned) to hold them together in a sheet..but the point is the thiner layers of wood can splinter more easily and usually will at some point. So sanding and bev eling "rounding" exposed corners of plywood should be considerred! But beve ling/sanding can be a good or bad thing depending on the type and grade of plywoods as well as the applications (among other things).
The edges of any plywood should be the main focus on any sealing applicatio n and should be double-coated/sealed at minimum! But I reccomend sealing ed ges lastly after the surface sheeting are sealed thoroughly so that any moi sture can escape from the edges as the sheet sides cures. Then coat the edg es and focus on them.
Now! In todays markets, there is a variety of alternative sealers, but in most c ases none of them reccomend use on plywoods due to the above and bleow reas on. Polyurethanes are more optionaly preferred than the exterior paints as an alternatives but not any more one way or the other. Most will say not re comended for ply woods, but cabinates often incorperate such as a protectiv e layer. Thus some/most urethans will say interior/exterior.
As suggested there is marine grade paints for wood as someone suggested as it is used on wooden boats and last a long time. But there is also the oth er alternatives and one I use that has not been suggested! Fiberglass Resins.
When I worked in boat manufacturing (too many years ago, Eb****d boats) the y incorperated fiberglass and coated it over plywood in their boats. Of cou rse the plywood was all treated grade plywoods (1/2", 3/4" & 1") on the tra nsoms and other areas as reinforcements! But the fact of the process was th at it was plywood "at the core hull" and the fiberglass and resins were app lied over all sides and edges as a sealer and as a strengthening,harder pro tection factor.
Yes that would be very expensive suggestion if the fiberglass is used in ad dition to the wood and you did mention your budget ideals. but you could sk ip the fiberglass and just use the resins to seal and water proof as a bond ing agent due to is verstile properties.
Fiberglass resin will last for years but it has no strength by itself so it will crack and chip when hardened (if flexed/stressed or hit/impact), thus the fiberglass sheeting/covers is used for strength in normal process and applicaiton. But the resin (I would think and suspect) is no different than applying an epoxy paint for garage floors or marine pain to a surface.... as long as it does not flex or is impacted harshly the surface will not cra ck and would be water proof.
Still, I think that epoxy paints for garage floors, marine paint, or uritha nes would suffice and be a better all around option cost wise (as long as i t does not flex). After all they epoxy paints are a derrived resin of diffe rent formulas and chemical make up; all with the same goal....TO SEAL. Bubb le Gum would work for christ sakes!
Focusing on Resins. The problem with using fiberglass resin is the fact that its inital window of cure time is very short (according to how much catalyst you add when mix ing). So it could start geling within minuts to an hour depending on the ty pe and mix. A few drops of catalyst (mixed with resin) can tacky-cure a cup of resin in about 20 mins and harden rubbery in 30 mins or less. The more you let it set the more hard and brittel it will become. Most common commer cial resin will cure tacky-hard (like fast dry Urethans) within 20-30 minut es and cure hard within 24 hrs. Plus the fumes! Awful! By the way----Such are the same factors you will encounter with 2 part epox y grage pains as well.
As everyone says, the problem with plywood is its core materials and edges, so any sealer would need to be applied to the edges as to help seal from a bsorbing moisture; that goes for any holes you drill so you would need to c onsider a slightly larger hole size as to accomodate a thin layer of sealer . You could also consider silicone caulk in the hidden areas as a extra pro tection.
I would menion the overlooked Polyurethanes but it will scratch and eventua lly give way to moisture, but it too is an alternative via (interior/exteri or brand). But you should be aware that there are two formulast of Urethanes (1) water base and (2) Oil based.... just like in paints. It is contraversal which one is better appled as a full sealer for plywood (cabinate grade) as the pro-con is considered. Water base will have a moisture content which will absorb into wood and add to the overall moisture level if entirely sandwiched/coated in the sealer all at once so a dry time and evaporation period should be considered for t he wood as well. Sealing the moisture in the plywood could cause the glues in the plywood to break down over time as the heat and cold are exposed.
Oil base will take longer to dry and a certain amount of oils may absorb in the wood as well, like wise maybe causing damage to the glues or wood over a period of time.
So its all your call but I hope this helps in some way.