What kind of threshold would you put here?

For the Bull nose I would use ceramic

I see a photo of ceramic tile and a wood floor. There already is a wood transition molding between the wood and ceramic tile. Your question is different than the photo.

Hi Jean, Looks like you just need to grout the area between the two rooms.

Good luck!

Rubber Mat or other mat - Kitchen side.......

i would go with the lighter color

I agree with Suzette Just put Grout there . The oak had a border on the edge already so it looks fine with out anything over the threshold to me ..I think they sell tube grout you can fill it in nice with out making a mess on the wood .But if not just mix the grout and put it in a zip lock bag and pipe it in the groves like decorating a cake smooth with your wet sponge and your done no mess on the wood

I would remove that strip of wood between the wood floor and tile. Purchase transition molding that overlaps both. Grout will not hold or last in contact with the wood. Comes in all wood tones.

I agree with William...but, purchase a length of oak and stain it to the color of the wood floor. Bevel the edges...this way you can drill holes into the oak and into the wood floor to screw it down. (drilling will prevent the wood from splitting. Also, put a heavy duty adhesive under the edge that sits over the tile. The reason for the bevel is a smoother transition so no one will trip. P.S. You can polyurethane the oak board before installing. We did this and it looks great!

I would use metel to go right over the seam