Tungsten vs Fluorescent vs LED photography lights

My brain is feeling a bit wrecked today. I've spent days researching which lights are the right lights to use to create pictures of my origami cranes to use to create product lines of t-shirts, prints, greeting cards, etc.

While I love shooting with natural light, it's not always going to be the best/most convenient choice. Of the three types of studio lights I've been considering (tungsten, fluorescent, and LED) there are pros and cons with each choice. So many that I can't decide which is the right choice for my needs.

I swear, the more I research the more confused I'm becoming.

Also while a light tent/shed (aka table top white box) would be good for close up shots, my mobiles are approximately 30" in height so I won't be able to use a tabletop box for everything. So, I've also been looking at softboxes.

The types of images I want to create are similar to the ones I created for my ArtPrize collateral. Shooting on a clean white background. . .

As well as close ups with simple backgrounds like this:

And this. . .

If you have any opinions about the type of light or brands of lights, kits, or bulbs you'd recommend they'd be appreciated. You can leave them here in the comments, email me, contact me through my website, or on Facebook if we're friends there.