0.8mm FR4, single or double sided is fairly cheap from places like ebay shops, and they'll cut it to size for you. As for encapsulating, nothing really beats epoxy resin
It's cheap, can be very clear, tough, and easy to use. Getting a all round perfectly flat (read: transparent) is difficult without a mold and polishing.
What I used to do for flat objects is buy sheets of clear acrylic, sandwich what you wish to embed between them (in your case, a PCB, my case, leaves or a silicon wafer) then fill it in with epoxy. As the refractive index of epoxy is so close to acrylic you won't see the 'join' and it'll appear as one solid block - plus you'll have both sides nicely polished already. Then you would only have to file/sand/polish the edges, which is FAR easier to do than a large flat surface. A dremel is recommended for a true polish job (buff wheel + toothpaste), but it can be done by hand with progressively higher grits of wet/dry paper, followed by a flame polish.
One more tip - if you're using molds, a great mold-release agent is parcel tape. I've never seen epoxy stick to the shiney side.
Apologies if someone has covered that already, I just skimmed the posts and wanted to add my two cents/pennies