Laminated stocks are not "plywood", in the sense of a 0,90 orientation for stability, like you find at home depot, or even an aviation supplier. They are a glue lam beam type material with all the laminations in the 0 axis. You can still achieve some stability by mixing grain orientation in the flitches of veneer. And the laminations make it much harder for moisture to migrate,
Epoxy is far and away the best option for just about anything structural, unless it is going to face fire. NASA used to buy wood epoxy composite windmill vanes from the Gougeon brothers, because it was the best bang for the buck until Graphite got into major production, and they still use the epoxy. Any brand of boat building epoxy, which is widely available, like west system, system 3, etc... Will not have any of the problems mentioned above. Bows are made with epoxy and the type used IS quite viscous which can mean visible glue lines. But boat building epoxies disappear in the glueline unless thickened, etc...
Vac bagging is always an advantage, but you need a fair amount of force to compress veneers, so you need a vane pump or better. Overall the laminations compress well, but a little squiggle in the grain can prove hard to compress, birdseye for instance.
A rifle stock is not so large that you couldn't either use something impressively heavy, or a lot of clamps. The idea isn't to get a lot of pressure, but an even degree of it that compresses all the gluelines. Weight is cool because it is self compensating. With clamps, tighten them firmly, then come back in a few minutes and snug them down again. Wrap in plastic to catch the glue, and use cauls top and bottom to evenly spread the pressure.
Titebond would be low on my list, but it is popular because it is available and cheap. If you have to spread a lot of veneers, be sure to use something like a roller, or notched trowel, get the glue on all surfaces fast, and keep them touching as soon as you can, or the glue can skin over. Epoxy isn't affected by the air, but you need enough cure time to get it done. Some epoxy hardeners give you half a day, but then they take longer to harden off.
Better glues than the polyurethanes, or Titebond, but not epoxies, are Weldwood plastic resin cement, and resorcinol. Of the two weldwood is easier to use, find, and glues without a dark line.