I need advice on portrait lighting equipment?

I'm fairly new to the world of photography and recently started receiving a lot of compliments on my work so far, I have even had a few people email me to set up photo shoots, and after looking at my work so far, they are willing to donate a decent amount of money. So my question is, I have an entry level Nikon D5100 and I was wondering what is the best lighting kit I can use to get great portrait shots indoors and out. Any custom equipment list would be greatly appreciated as well.

I'm a full time student and single father to two kids so I'm extremely limited on my budget. Any advice would be greatly appreciated.

Added (1). This work really inspired me so these are the results I would like to get.

A good start would be to base a system around speedlights - they are battery operated, lightweight & portable. A fully manual speedlight like the YN560 costs around £50-60. A light stand about £15 and modifiers (umbrella or softbox) would be about £45. A 24" softbox would be about right. If you are in the UK I can recommend Cotswold Photo on eBay for most of this stuff.

A speedlight system means you are not dependent on mains power - so they're handy for location shooting outdoors or at clients homes.

A 5-in-1 reflector (about £10) would also be handy for fill.

To trigger the lights I'd recommend RF602 radio triggers - about £20 a set. Good range & reliability, even outdoors.

You should also invest in some good portrait lenses if all you have is the kit lens. I'd recommend the 50mm f1.8, the 85mm f1.8 and a 24-70mm f2.8.

If you are new to off camera flash, have a read of the Strobist blog - the Lighting 101 & 102 archives (drop down boxes, lower right of page) are a great resource;
http://strobist.blogspot.co.uk/2006/03/lighting-101.html