I painted one other piece of furniture in our house with oil based paint and even though it was a little more work to clean up, its worth it because the finish is super durable. Oil based paint has another perk, it is self leveling. You don't see a ton of brush strokes or roller marks. After it dries it is smooth and glossy.
I put Cameron to work on the painting portion since the stuff is super stinky and considering I'm expecting it wouldn't be very healthy for the baby. Since I painted with oil based paint before I knew some tips which I learned the hard way and suggested them to Cam. He did great. In case you ever feel like trying it here's what we've learned...
Once you go over an area resist the urge to go back in the same painting session and touch up a spot. It will leave the brush strokes.
It's better go thick with the paint (not so much that it drips though). And believe it or not a brush actually works better than a roller.
We used oil based primer plus two coats paint. Here is its now. I got the new pulls from home depot.