Once again, a softbox is a type of
modifier that you mount on the light. It's a fabric 'reflector' (pyramid shape) with one or more diffusion panels to get an even distribution of light. You mount either a flash or a continuous light source in it, and the softbox makes the source larger (compare the surface area of the front of the softbox with the surface area of your light). So a softbox is not cheaper than a flash system, a softbox is used with a flash or continuous system. Those other things are light tents, and are good for a very even, boring illumination. A light tent is also used with either flash or continuous lights.
I'm not sure if completely illumination is optimal, I'd think you wouldn't want that much light reflecting from the top of the parts, since a direct reflection tends to obscure markings. For example, about half of the devices on
this PCB have their markings obscured by direct reflections.
This picture (water optional) with the main light from camera right has all markings clearly visible. But I'm sure you'll get acceptable pictures with completely flat lighting in a light tent.
And yes, proprietary flashes with all the automation are expensive, but there are manual-only flashes available for $50 or so (search
the Strobist site for recommendations), although studio flashes are a lot nicer for this kind of work (where you don't need the portability). You could probably also get a set of cheap studio flashes for $180.
Continuous lights are easier to use (although the modeling light on studio flashes helps), but don't put out much light compared to similar-sized flashes. Not a problem as long as your subject is stationary, your camera is on a decent tripod and you don't have much ambient light to mess things up.