Mary Ellen used particle board for the base (peg board with the holes already drilled every inch is a good surface, and can be mounted with screws in the holes that show through). This is also a good way to size up your image, using the one inch grid already there with the holes.  She attached the caps initially with poster tac, to position them.  When she had a section I was happy with, she used a hot glue gun to permanently attach them.

You cannot use craft-store hot glue sticks, they don’t have the binding material you need. You must use industrial glue. You will need a high temp glue gun. You need to make sure the glue is at hottest melt to really stick.

Caps can be made of 5 different chemical compositions, some are more durable and some are more brittle. Omni Bond is the only glue she found which adheres to all those types. Be aware that plastic is not archival, it will fade and crack especially if put in sunlight.

One more thing:  you must carefully wash and sanitize each cap. Rinsing isn’t enough, even if it looks clean. Otherwise, you could attract a lot of roaches and other insects and such. Mary Ellen washes her caps by hand, or put them in a mesh bag in the washing machine on gentle. Soaking them for a bit in the pre-wash cycle can help.