You could group them any way rocks are grouped. I think the best way is geographically. Your favorite specimens from everywhere you've been, organized in a way you can tell the story how you came by the specimen. Crystals, gems, ores, fossils and rock.
I like agates, I keep my agates separate, since they are my favorite. I keep fossils separate. I keep my semi precious stones separate. To be honest, I have so many, I have to keep my current finds out to complete identifications. Many times searching the beaches I keep samples of the rocks so I can show people how to tell what they are.
Crystals tell lots of stories. Some rocks glow luminescently. Some are sedimentary. Some are volcanic. Thet all tell stories to me. So sedimentary rocks are grouped together. Concretions together. Crystals together. Magnetic together. Igneous together.
My rock groups are mostly from the great lakes, but we have basalt and other igneous rocks. We have sedimentary rock, we have rocks from alluvial flow. We have Sea rocks. We have giant salt deposits. We have vast mineral deposits of iron and copper. The rocks I have tell the geological history of the great lakes. I group them in ways to tell that story. Other areas of the country would do it differently to tell the same story of their geological past.
The story is as important as the specimen. I learned about luminescent rocks at the Seaman Museum in Houghton, Michigan. I also looked at real meteorites and learned so much more about them at the same museum on the Campus of Michigan Tech. I learned about the Lake Superior fault and the formation of what is now Lake Superior from the trip to the world's largest amethyst mine in Canada. I followed that volcanic history down the Black River and it's seven waterfalls where I walked on ancient lava flows. I picked up agates on beaches around Michigan, looked for Greenstone near Duluth and picked up Petoskey stones from Lake Michigan. I visited the Copper mines and the iron mines of the upper peninsula of Michigan. I walked the shores of lake Michigan and Lake Erie collecting fossils. I learned about alluvial flows after finding a two hundred and fifty pound puddingstone in my yard. This prompted me to learn about glacial periods and concretions and conglomerates. I went to Indiana, Ohio and Kentucky to visit fossil formations. I went to Mammoth cave and Lost River cave and learned about cave systems and bats. Learned about stalgmites and stalagtites, limestone and calcite formations.
The long and short of it is if looking for arrowheads got you into rocks, then learning about obsidian, flint and chert got you started. Then telling that story is important. Finding out the flint, chert, jasper, quartz, chalcedony and agate are all silicates and share similar properties and the same chemical formula, made you keep looking. It drew you in and your collection should reflect it. If semi precious stones at rock shows got you there, then that's where you start.
Odds are if it intrigued you, it will fascinate the people you show your collection.