this is the "style" of gun display cabinets I made back in the '70s and '80s.
the common wood would be red cedar or cherry. occasionally red oak.
I had a friend that owned a glass company nearby and I purchased my
custom cut glass from him. I always used the laminated tempered glass
with the plastic film in the middle or the gold chicken wire between the
normally, it was just the simple desk type of key lock. just to keep the
kids out, not from a burglar.
on some, I installed a simple 1/8" aircraft cable (painted black) that went
through the trigger guards and discreetly wound down the insides of the top
cabinet into the inside of the base cabinet and secured with a padlock.
this was a full loop cable - the ends were not connected to an eye bolt with
screws that could be easily yanked out with a stout tug.
so a burglar would have to haul the whole cabinet outside to get away with it.
and no, this was not designed to be a "gun safe" it is a "display cabinet".
you can argue "home security" and "home invasion" all day long - but let's not.
the original question was how to secure the top cabinet to the base cabinet.
there are several methods as options - let's hear yours.
and for the screws to marry the two together, I would suggest a flat washer
style of screw - or use washers with the screws you use.
similar to the GRK screws that are often used in furniture making.