Near natural lighting with softbox wattage between 2400 to 2700?
Wattage has nothing to do with achieving natural lighting.  The amount of diffusion and placement does.  More light is ALWAYS better because it results in more signal to the camera and more options as far as ISO, aperture and shutter speed.  

Nothing you setup with artificial lights (particularly on your budget) will come close to the level of the sun on even a cloudy day.  This doesn't matter though as long as you provide enough light for the camera to pick it up and spread it out through diffusers and light placement and reflectors such that you get a natural look.

I'd suggest reading some on 3 point lighting if you want more information on light placement and get the biggest diffusers you can, though on your budget, you will be hard pressed to get even a decent 3 point light kit, let alone any kind of diffusers.  (A decent large diffuser alone will run over $100.)  Your best bet is to put all the money in to the best light kit you can get and get diffusers later.  Proper three point lighting will still be fairly natural looking.