Welcome to the forum.
A softbox 'softens' the light, but it can still create shadows, depending on the angles between the light and the subject and the camera. To get very even lighting, you will likely want two lights.
Keep in mind that flat or even lighting isn't always what you might want. No shadows can also mean that you won't see the texture.
Also, a softbox or an umbrella are just light modifiers....they are not lights. First you have to decide if you want constant lighting (tungsten, florescent, halogen etc.) or if you want flash/strobe lights. You could use either but I'd suggest flash/strobes if you are going to be shooting models (things that move).
As for the backdrop, are you planning on extracting the models from the background, and replacing them onto some other background? If so, why? Or do you just want to have the model on a clean background? Either way, using a green or blue screen may be more trouble that it's worth and really isn't necessary. You can extract a subject from a white, black or grey background pretty easily, as long as you light them to prevent them from merging with it. And if you just want a clean background, then just shoot them on that background and save all the post processing work of extracting them.
I'm guessing that the kits you are seeing, are the cheap ones (only a couple hundred for the whole kit). Like with most things, you get what you pay for....and if you cheap out, you will likely end up with poor results or you will end up paying more for better gear down the road.
Lastly, have you considered just hiring a photographer to shoot your product line? Many successful business people will tell you to stick to your strengths and outsource the things that you can't do as well.