Isaac, I think the colorful stones are semi-precious stones, I think they have been made into cabochons. The other specimens are very difficult to ascertain. There are a few tests you can do. If you can scratch them with a pocket knife, it probably isn't a gem. Once you determine that, you can see if the specimens will scratch glass. Emerald, diamond, sapphire are all very hard. Really your best option would be to take them to a jeweler who could tell you about the value and composition of each.