First let me start with a disclaimer: I am not a professional photographer. Since I do not rely on my equipment for my job, I can afford an occasional snafu. This allows me to pick more affordable equipment, which I will described hereafter in the most affordable option.
I started my studio photography years ago in the basement of my parent's house while at college I had two 500 watt halogen lamps and a wood panel which I used as a background and occasionally painted in different shades of gray. I was using black-and-white Ilford FP4 films, so I really did not care about light temperature.
From Nina's friends collection - Eric Raeber 1989
two 500 watt halogen lamps and a tungsten table lamp
Ilford FP4 135-36 125iso
Before you purchase any studio equipment, you have to ask yourself what type of photography you intend on doing:
Do you have a dedicated location for your studio?
If you setup your studio in your living room as I do, you need to consider how easy it is to deploy and fold it back. Otherwise you will hesitate before taking it out. A softbox is more difficult to fold than an umbrella.
A paper seamless background is more difficult to mount and to store than a muslin cloth or just a plain wall.
Do you travel with your gear?
If you do travel, consider the power supply: the 4 AA batteries in a speedlight are easier to carry alon and replace than finding an AC power or carrying an AC battery pack
Consider also how much space your light stands, umbrellas and tripod will take when folded into the suitcase or carry-on on that plane to paradise!
Do you shoot outside?
If you want to shoot in/against the sun, you will want to overpower the sun. Speedlites will not be sufficient. Especially if you intend to use a light modifier. You will need to use monolights 300 W/S or more.
Do you shoot people?
If you shoot mostly inanimate objects, you have all the time in the world with your shutter speed. You can even use a flashlight! If you shoot people and you decide to use a copntinuous light, you will need to work at relatively slow speeds (1/60th) or open your aperture way up to catch that quick smile. I have never used continuous light.
Do you shoot action?
If you want to catch that hair in motion or do dance photography, your standard strobes will bee too slow. Unlike the speedlight which have a thyristor to stop give a light pulse, strobes generally have a "slow" (1/300th) exponential discharge through a capacitor. Bottom line if you want to freeze action, you need to use a speedlite at 1/2 power or some high end strobes as I describe in the 5th option below.
Do you shoot large groups?
If you shoot groups of 2 or more. You will need something with more power that a speedlite.
Now that you have figured out what you want to shoot (or let's assume you did), let me take you through equipment I would purchase for a relatively general purpose photography in a temporary studio, with the ability to carry around and do some occasional action shots.
I will try to describe the studio equipment in increments, which allow you to start with a really tight budget. I will assume you already own a tripod, which is an absolute most both for long exposures as well as for taking multiple shots that you intend to superpose. The entry models start at $45: Dolica 62"
The very first stage for studio photography, which is also the cheapest is to "paint" your subject with a flashlight. This is perfect for tabletop photography of inanimate objects such as flowers, etc. It requires very minimal equipment which you may already own:
Note that the use of an LED flashlight is important, because it has a similar light temperature to sunlight or to flash strobes, which allow you to mix lights
The next best cheapest option to cover a larger studio area is to use continuous lighting. I have personally never tested that out as the limited amount of light these simple lamps produce require a high iso, a very open shutter or a slow speed.
If you decide to purchase this kit and later want to move on, the light stands and umbrella will still be useful.
Light painting - Eric Raeber 2013
This is equipment everyone interested in studio photography should purchase. Even if you decide to move on to option 5 or 6. You will always use your speedlite as an auxiliary light and you will carry it with you for extra light traveling.
When you start feeling limitations because you only have one light, use the foam board from option 1 and hold it on the other side of your subject to reflect the light. This will approximate the effect of a second light source.
When you start feeling really too limited after trying every combination of speedlite and fioam board, it is time to move on. You can choose two routes. If you want a very lightweight studio equipment which you can carry around, purchase a couple more speedlites (option 3). If you think you want to get serious with large studio setups or more powerful lights, go to option 4.
Here is some equipment you will want to consider to grow your speedlite setup:
When you want powerful studio strobes, you are looking around or above $200 for a 400 watt/seconds strobe unit. I have had good experience with Visico but they do not seem widely available any more. I have tried cheaper units in the past (around $120) but they tend to have custom accessories, they don't last and the you will have difficulty finding replacement bulbs. Here are a few things to look for:
If you intend to later upgrade to Option 6, you may want to consider AlienBee units which have compatible accessory ring.
Expect your budget to be in the range of:
If you need powerful stobes that have a very short flash duration to capture motion, your most affordable choice are the Einstein E640 units by Paul C. Buff
I have described just that one route I took with my studio. Many more options are available. So add a comment to this page to either to share your own experience or to ask for clarification on any topic I have addressed here.
Single speedlight in a 60x90cm softbox - Eric Raeber 2013
Dance Photography - Eric Raeber 2012
Two Einstein E640 with 64" umbrella