Thank you for your question about chair casters. I think we can help you.
First, we can narrow down wheel style. All wood floors require soft wheel casters. These won't damage your floor, and and prevent your chair from sliding around too much on the smooth surface.
Figuring out the right stem is a little trickier. The first thing to do is check out the chair base. Is it wood, metal, or wood clad (metal with a wood or simulated wood cover)?
If your chair has a wooden base, you'll need W stems. You can order soft wheel W Stem Casters here.
If your chair has a metal or wood clad base, you'll have to remove one of your current casters and measure the stem. The best way to measure the diameter is to wrap a string around the stem, then measure that length. Most stems have either a 7/16" or 3/8" diameter. After measuring the diameter, measure the length to get the proper stem type.
If your current stem is longer than the options in the diagram, that's ok. You can use a stem shorter than your original. Only the diameters have to match.
Hope this answers your question!