TWO equally-powerful light sources if used not quite properly, can create unappealing, odd-looking, conflicting shadows, one shadow on one side of say a spray cooking oil can, and another shadow on the opposite side...that is the biggest danger of using two lights for a person who places two lights in a simple "45-degree equal" type setup or who does not know how to light with a main and a fill-light.
I looked at several of the linked images...most are diffused light, flash most likely, but it doesn't have to be flash lighting...some have good balance with light fixtures, so, likely tripod-mouinted camera, well-aligned camera, back of camera parallell to back wall, etc.etc.. DIFFUSED lighting in most cases; the density of the sahdows and the crispness of the shadows varies; some were shot with a large, well-diffused light source, others a smaller source. With timed exposures, an LED light and a diffusing material could be used.
A flat-faced, recessed face softbox, made in China model, and a flash unit and a light stand would be the basics, plus a camera and lens. Other options would be a PVC pipe frame, fitted with a tightly-stretched piece of white, semi-transparent ripstop nylon cloth from a fabric store, about a 30 x 30 in ch frame, or an even bigger frame, like 42 x 42 inches, a way to hold that in place, and a way to fire a flash unit through that PVC-and-cloth-fabric diffusing panel.
You want mostly-diffused flash illumnination...not hard-edged shadows, but shadows that are somewhat soft, yet which exist, to show the shape and texture of objects....a smallish 24 x 24 inch softbox will be adequate at diffusing at closet-type distances I think. Softboxes: easier to get into smaller areas; umbrellas; curved surface can make reflection control tough for the beginning shooter, and are fairly large and hard to cram into some small areas.
The MOST-basic option could be a smallish mini-softbox, like a 10 x10 incher, a TTL remote strobe connecting cord (like the Nikon SC-28 for one example or a generic for your camera), a $79 Neewer brand speedlight flash, and aiming that flash at the closet/pantry, and getting moderately-diffused light that has "some" soft shadowing, which will show the shapes of shoes/cans/bottles, etc. Hold flash and small mini-softbox in left hand, aim flash at scene, shoot with right hand, all done single-handedly...
As always--research/learning/videos/how-to articles/photographer education, all can be helpful. Learning about light and lighting is the key to this genre; it's NOT high-end lighting, mostly just diffused light, and good, leveled-up, not-crooked camera work.
You might be able to hack-rig some other diffusing stuff....like a flash + a gallon milk jug, or a flash + waxed paper sheeting, or a larger Tupperware contained with the flash tucked under it,etc..
You could do much work in this closet/panty genre with just ONE, decently-diffused, nice light source!
