Don't use a latex stain. It will peel very quickly. The Tred-Plex will work well. Make sure to use the recommended primer and apply 2 coats. Another alternative is to use oil based solid color deck stain. This will be durable and easy to maintain. Plus, no primer is needed.
You don't have to be overly concerned about the remaining paint. If it isn't peeling then everything will be fine.