New internal door sill for step down to new addition to house

Hi,
I have added an enclosed room to the house which is a lower level, 1 step down, to the existing building. Entry to this room is through what was a cupboard. I have managed to find a couple of doors that will fill the space and will build in a door frame to suit. I have searched this forum which is where I usually find my answers to tricky questions but no luck this time.
My question is what to do at the bottom of the door. The floor boards extend to the edge of the step and as the old area will be carpeted I feel I need a door sill so the carpet has something to butt up to. What do you suggest re the type of timber I should use and what thickness should it be.
The 2 doors will swing opposite ways so one will be over the carpet. This may have a bearing on the height of the sill.
I look forward to your suggestions.