My pantry is ~4' x 4' - give or take a few inches. We have a single flourescent light (looks to be 18") and I have no lighting problems at all. In that small of a space, I think placement of the light is more important than type of light. Even with a recessed can, pull it away from the shelving. Don't center on ceiling. It will not light things from the front well.

I have a corner step-in pantry similar in size to your dimensions. The lighting designer I consulted for free at the local lighting store told me to put a fluorescent light bar over the doorway on the inside. I think my sparky used an 18" (could be 24"--I'm too tired to get up and look) bar. The room seems very well lit. I would probably have stuck a can in there also had I not been told otherwise. I'm glad I listened to the designer as being in the room now that its done seems like a can wouldn't have been the right choice for best illumination. And I hate fluorescents so that's saying something!

Our pantry is 5'x7'. I brought a semi-flush vintage fixture from our last house (it was in the foyer). One bulb, glass shade. It gives out plenty of light.

Recessed lighting is somewhat directional. As a result, a single recessed can is not likely to provide you with enough light.
You'll be best off with either a flush mount fixture or, as others have recommended, a small flourescent light mounted above the door.
A feature you'll want to consider is a switch that will turn the light on automatically when the door is opened.

My old 5 x 10 pantry had a 4' fluorescent light in the center. Enough light when the fluorescent worked. The lighting store told me that fluorescents do not ''like'' to be turned on and off frequently. Tends to wear out the ballast (I think that's what she said.) Ballasts are pricey and I hate flickering fluorescents!

Anyway, I replaced it. I did not want can lights because they leave the ceiling unlit. Their downward spreading cone of light also does not light walls and shelves that are close to the light and near the ceiling. Pantries are confining enough without dark ceilings. I used two (you will only need one, I think) flush mount fixtures, each with 3 bulbs. LOTS of light, but that is what I wanted.

Maybe modern fluorescents can be had that are more amenable to the frequent off and on that a pantry, mine anyway, demands.

I second the idea of a switch that turns the light on when you open the door. After all, you will probably not want to be in the pantry with the door closed, and when your hands are full, it's nice to push the door open and have the light come on automatically.

I was told that newer fluorescents are better than the older ones. Or maybe that was just a sales tactic to get me agree on one because I do not like the.

In a pantry as large and as decoratively beautiful as Allison's, a ceiling fixture could work. In my small corner pantry, many shelves line the two long walls. Its much more crowded with storage than Allison's, and I have storage up to the ceiling. Seeing how my other cans behave, I know I would not have been happy with one in there.

We have a 30" x 38" pantry. Our pantry is not step in though and the shelves from waste level down come all the way out to the edge. From tummy level up they start stepping in slightly (in a U shape) so you can see and reach what is on the upper shelves.

Hubby is in the process of putting lighting in for me (if he ever finishes making the doors). Our doors are off center. We are running LED puck lights down the wider hidden side (if that makes sense) of the door. They will turn on when the door is opened and there will be one light per shelf aimed out at the shelves.

I have a 4ftx4ft walk in pantry. We put in an 18" round fluorescent that is automatic on when the door opens stays on for about five min after door closed. Motion sensor. LOVE it. I hate flo lights. Plenty of lighttho and instant on and really cheap. Round frosted glass cover so it doesnt look like a shop light.
Motion sensor is The best for the pantry
Its been five years and still the same bulbs.