Well, you need lights of course, but above all you need to understand the lighting process. The kit that you linked to includes 3 (terrible) lights, simply because most people think like you and go for a solution in a box, but it's actually harder to start off with 3 lights simply because you'll inevitably make mistakes and you won't know which light is doing what, and where the problem is coming from, so the best bet, for most people most of the time, is to start with one good light (a studio flash) plus a reflector - the reflector can often do the job of a second light and, if the bug gets you and you want to go further, buy a second light and maybe a third - that's about as many as you're ever likely to want to use on the actual subject, although extra lighting is always going to need to be used on the background, unless you want it to be black.
To save time, here's a quick copy and paste from my book "Lighting Magic" - hope it helps.
"Use just one light
“Natural” lighting is light that looks natural. Typically, if you take a shot outdoors using the sun as the light source, the sun will be fairly high in the sky so the light will come from more or less above and the shadows will angle downwards. Indoors, much the same applies, because typical room lighting is positioned high. Therefore, if you want your flash shots to look natural, place the light high in relation to your subject.
There can be practical limitations to this if your ceiling is low, and the easy way to get around this is to avoid shots of people standing, because you may not always be able to get the light high enough. Always remember that, regardless of how many lights you use, just one light does nearly all the work (usually between 80 – 90%) and that any other lights that you use are just making relatively small changes.
The light that does nearly all the work is called the Key Light, and this is the one that is normally set high up, to create the natural look, and it is typically placed directly in front of where your subject is facing. This means that if your subject is facing your camera, the starting point for the key light is likely to be directly above your camera, and if the person is at an angle to the camera then the light will typically be in front of where their head is pointing.
Never, ever, use a ‘standard lighting setup’ because it can never produce anything better than mediocre results and which is about as creative as “Painting By Numbers” – the lighting needs to be arranged to suit both the effect that you want it to produce and the qualities of your subject. For example, lighting that suits a beautiful woman with perfect skin isn’t likely to be work well on an old man who has spent his life working outdoors in all weather conditions…
The lighting process
It doesn’t matter how many lights you have, what your subject is, how much space you have or how much experience you have, the process to follow is always:
1. Know the purpose of the shot.
2. Decide on the look you want to achieve.
3. Get your subject in the right place and in the pose that you’re going to start with.
4. Get your camera in the right place, with the lens that’s going to place it at the distance that will produce the right perspective for you, and at the height that you’re going to shoot at.
5. Leave the lighting until last because, although it may be the most important single ingredient, the positioning needed for the lighting is affected by everything else. So, at this point you should arrange the key light in the place where it produces the qualities you want, ignore any ‘faults’ for now.
6. Adjust exposure, using flash power and/or lens aperture and/or ISO setting at this stage, because severe under or overexposure will exaggerate or hide lighting problems.
7. If you want an effect light, for example a hair light, introduce that now. Adjust its position and power and take test shots until you’re happy with the result.
8. If you need a Fill light (because although the shadows are in the right places, they are too strong for your taste) introduce it now. Typically, a Fill light is best when it is an on axis fill, i.e. in line with your camera lens, not off to one side.
9. Start with the Fill light at far less power than the key light, take a test shot and if necessary increase the power and then take another test shot. Keep doing that until you’re happy, this is much better than having a Fill light that’s too powerful.
10. Adjust power until either your flash meter or camera histogram tells you that the exposure is where it needs to be.
The purpose of the shot probably needs explaining, and getting it right is vital. For example, you may want to photograph a product to sell online and need photos that show exactly what it looks like, warts and all. Or the photo may be needed to show the product at its best, with a very different approach, making it look as desirable as possible, often at the expense of accuracy.
And it’s the same with people. If someone wants you to photograph them then you need to know why they need the photo. Once we become adult and start moving through life, we all tend to have different identities that are visible to different people. For example your subject may want the photo to show that she or he is
A loving parent
An exciting lover
A skilled worker
A friendly, caring person
And so on. Knowing the purpose of the shot, before you start, will affect both the pose and the lighting.
Job done, or at least the lighting is now functional, but don’t be afraid to experiment with different lighting to get different effects.
Lighting can get a lot more complicated than that, but if you remember the one, simple principle that I’m going to tell you about now, it will always be simple, and it will always be magical too.
That principle is that there is only one sun on this planet, so we try to use only light. Other lights are added only if necessary, either to correct problems or to create special effects, but never routinely."
Going back to your question, a background can be almost anything. Getting a massive sheet of ply and painting it is certainly a solution, although a cumbersome one. The "Goalpost" background supports that a lot of people buy are certainly more convenient but most of them are just about adequate for paper backgrounds, which don't last long, or for muslin ones, which crease badly - however muslin is the best affordable choice for black. Decent quality vinyl is far too heavy for most of these background supports.
But do you actually need a background at all? Many of the best portraits are environmental ones, i.e. taken against a natural roomset background. Personally I don't see anything particularly professional about using a studio background, they do have their uses but the results often look stereotyped and artificial.
Makeover style shots are a bit of a cliche, hopefully they've pretty much had their day now, although of course there are still a lot of people making money from them.
). Anything cheap off ebay is probably going to be folded and so unless you can get your subject a good distance from the background so shallow DoF throws the background out of focus, any little wrinkle, fold or imperfection will show up and need editing out in PP. Rolled paper or vinyl plus stands would be better but a bit more costly. That said There must be somewhere in your house where you can find enough un-cluttered wall for a head shot, even if you have to move chairs and take a painting off the wall, as Phil says get some practice before you start worrying too much about backdrops.