"Flash will give an overall artificial look"
words of an inexperienced studio photographer
Quite honestly, save your money. Anything you get with that budget, will be trash, and quite useless.
If you are going to shoot portraiture do NOT get continuous lighting. Your shutter speeds will still be too low or you will have to use Iso's that are too high. Your models will sweat. The power consumption is ridiculous. Continuous lighting is archaic and has its place today ONLY with product photography... quite frankly only a fool would use these sorts of lights for portraiture work.
Strobes produce the same exact light as continuous-lighting. Except it is day-light balanced, and offers much more control and fine-tuning. Your modifiers are what determine the quality of light, this makes no difference whether the light is continuous or a strobe.
For a portraiture setup, the bare minimum you would need is one strobe with a softbox, and a reflector. Add more as budget allows.
Go to www.alienbees.com
and look at their range of monolights. They are cheap, reliable, and perform well. If you get anything less than these, you will regret it. Most of those cheap all in one studio kits, provide you lights with incredibly inconsistent color and exposure, horrible build quality, and super-weak power. One has to consider how much more power is required once you put a softbox on the light.
I use 3 AB800s with one softbox, reflector, and grids for the most part. You can see my work here: www.fkwstudio.com
Sony A850 | Sony Battery Grip | Carl Zeiss 24-70 Vario-Sonnar T f/2.8 | Sony 70-200G f/2.8 SSM | Lensbaby Composer Pro | Sony HVL-F58AM
Alienbees B800 (x3) | Alienbees Cyber Commander | CSR+ Receivers | Grids, Softbox, Gels, Manfrotto/Century/Avenger stands