Yes, get the10 or possibly 12k& a good strop. A SRD latigo3" with fabric will suit your needs. Also a crayon of chromium oxide to put on the fabric of the strop.
Guarantee you will be amazed at the difference.
You've basically described how i started years ago.
They are a little expensive, and took a little time to buy them all , but the naniwa stones are worth it. But i use the1-5-8-12k super stones. Then cro/ox on fabric. Then fabric. Then leather. I was amazed at the difference of the shave compared to what i thought was a good edge.YMMV , but i doubt youll have any remorse or guilt.
Remember to lap your stones and bevel the edges before you use them.
Lapping stones are cheap.

Happy shaves
Mike