Light travels in straight lines but can be bounced, reflected, defused and softened. Getting your head around this concept is the fundamental skills to portraitist photography and is equally applicable to natural light, portable flash gun or studio flash.
It's well worth practising with natural light and a simple reflector / defuser to learn the basics. A good place to start is Rembrandt lighting which is a classic technique. A single light source being the sun with a reflector. It's subtle and the results are just as pleasing and relevant today.
Even the most complex lighting setup starts with the application of one key light and then others are added to get the desired effect.
A flashgun would be the next logical investment and offers up a whole hole host of creative possibilities with a diffuser, soft box etc when deployed off-camera combined with the reflector. The advantage of this it's small portable and can be used equally well outside and in.
We can get as complicated as you like on lighting but my advice is start off on the basics and then build on these skills, you will find your knowledge and confidence grows. Whilst photographing your subject it's important to maintain a rapport and keep them engaged, if you are concentrating two much on multiple lights they will soon get bored and uncomfortable and you will loose the opportunity and the moment.
Having grasped the fundamentals then you can make some further decisions on expanding your flash guns or obtaining studio flash within your budget.
