I've created several of them with no real problems.
The first was done without benefit of a Oneway Termite Tool. While it came out just fine, let me strongly suggest you have a tool for end grain cutting. It sure makes it a whole lot easier.
As for advise, the best I can offer is to go slowly, and very frequently check the fit. Matching the inside of the wood with the outside of the stainless insert is pretty tricky, but is best done by small cuts and checks for fit.
As for finish, I used Famowood Glaze Coat. It's an epoxy coating used commonly on bar tops. I apply it inside and outside the wood effectively sealing the wood against any moisture from drinks or hand washing of the mug.
Best of luck,
Jim