Let the stain dry according to the stain directions. Then paint a small are to see if the stain bleeds thru. If it does use a stain blocker like Kilz, let dry, sand lightly with something close to 220 grit then paint. Another sure way to do it is let the stain dry, give it one coat with whatever clear you were going to use, let that dry, lightly sand it (same grit as above) then paint over. Bottom line is the stain needs to dry. The paint might seal in the stain, might not that's why you need to test the paint, no loss there. The clear or stain blocking primer like Kilz will seal the stain for sure. As far as lightly sanding (scuffing) you need to do that with paint, clear, primer or sealer. The reason for that is whatever finish you put on wood will raise the grain causing all your other top coats to feel and look rough. If you lightly sand after first coat the final coat will look a lot better. Good luck.
You need to sand the wood first, scuffing it up, clean it with tsp, apply a good quality bonding primer, then you can top coat with a premium paint (enamel). Sherwin Williams has a great selection of bonding primers, ment to go over stained(varnished) surfaces.