First the nightstand:
Depending on what the current paint and surface condition is will decide what process you need to use.
The basic rule of thumb though whether the paint is flaking, dipped, rippled or perfect condition do as follows:
Give it just a quick surface sanding to give the new paint and primer finish something to grab (100 grit sandpaper) , prime and paint.
Use just a regular latex house paint, any brand will do. Make sure to coat well even if you need more than one coat. Choose a flat versus a high gloss so it will be more durable, unless you want to use high gloss. In that case you will need to seal with some kind of sealer like Polyurethane.
Second the wine rack:
Sand with 100 grit to also give grip to the new paint, prime then paint as with the nightstand.
Good luck, and I hope this all helps.