Usually we drill holes in them and make necklaces for football games.

However, I did manage to save some buckeyes from my bottlebrush and just keep them in a bowl on my desk. In the past, I have just kept regular buckeyes in bowls as decorations. They last for years.

My only warning is to watch the squirrels. They will get into the pots and dig up the seed even after they have sprouted. They will drag the little trees all over.

I do not know about preserving them, but I assume you are not going to grow them  buckeyes need to be planted fresh. Keep them out of plastic bags or they will mold.