I'll try to make it short and easy to understand .

There are 2 kinds of setups:

1. Hot lights -  Consist  of powerful bulbs. They get hot pretty quickly and are pain to work with. Would not recommend for small studios due to lots of heat they produce. God forbid you drop on of those on a model. Generally not very powerful(unless you are a video production company...). If you can work with those, go ahead and buy it. In the winter,maybe you can turn off your heat and use these instead....(this is where you  are suppose to smile :) )

2. Strobes - flash type units that work the same as your on camera flash,but with MUCH more power. They don't produce heat and can output a lot of light. They power is measured in watt/second or ws.  There's no 1 global standard though. Some companies measure their light differently,thus you can see a 60ws light advertised as such,when in fact it's about 30ws... This is especially true for cheap or no name units,that try to get you to buy them. All the high quality units are more closely measured(still different...). One thing to  watch out for is Watts. As you may already know,Watts don't mean how bright your lights are,but a measure of how much power they drain. An energy saving bulb of 150watts can outshine 300watt bulb very easy.

Questions.

 What's good?  Well, as with everything, the more money you spend the better quality you get. There are units for professional photographers on which you can spend $2000+ for 1 strobe.  There are also companies that market to semi-pro photographers at very affordable cost. Look into Alien Bee,SP-System,Speedotron.   I would personally go for Alien Bee units due to exceptional customer service and warrantee they provide+ they are made in US.

How many should I get?

I would really recommend starting with 1 strobe and upgrading as you go. Once you learn all the lighting techniques with 1 light,you can start upgrading to 2 and more lights-as you see fit.

I see different accessories, which one do I need?

Well, Softboxes in general,produce the softest light(shadowless). They take a bit of time to assemble.  Umbrellas can be shoot through or reflected. They(in general) provide a bit harsher light,but easy to carry,assemble and use.  There are also grids that can narrow the light angles(say to just light up your head,but not the rest of the body). They are measured in degrees and generally are sold as 10-40degrees.

Can I just shoot with no softbox or umbrella?

Yes! you sure can!   Start as is and upgrade as you see fit...

Light stands? 

Get the best you can afford. Lights are expensive and heavy. Don't rely on a $40 light stand. Get a heavy duty stand. 

I see very cheap lights sold here,on ebay. Should I buy them?

There are many lights that are sold here,including kits with many lights. I prefer buying something once and not upgrading it a few months down the road.  Check for their warrantee.  A quality light can output 100,000s of flashes before needing a new flash bulb.  Some cheap lights are only good for about 5-10K.  See how much it would cost to get a new one.  Sometimes I shoot about 1000 pictures a day,using a strobe. Having to replace my bulb every 5 days would not be an option...


Last,before we finish. Don't just buy something. Research first! Be an educated buyer. Don't just buy because it looks good or the ad says you should buy it :)

Later,

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