I keep a large strop in the kitchen. Each knife gets a few strops before being put back into the knife block. Works very well and most importantly keeps my wife happy as she hates blunt knives.
The fine stone I have is a Shapton 2k. I was planning on getting some finer ones but then came across some really good diamond pastes. I treated a few strops with 2k, 4k, 8k and 50k paste.
I now use those to bring edges back if they need more than a bare leather strop.
As mentioned before, how you prepare the leather before making a strop is most important. See Steve Kramer's valuable instructions
here.