You do not need professional umbrella kits or soft boxes really. You can use medusa lamps, ikea lamps, or even just desk lamps. Lots of girls do. And if you're in a small space umbrella lights aren't even gonna work cause they have to be set back from you.
So step one would be realizing how to light yourself. Basically you need to be surrounded by it. Like they're stalking you. Being lit from every angle means no shadows and shadows are the fucking devil man. So say you have Davids set up of just straight on like at a desk you're gonna want one on either side of you and one to light up behind you. 2 simple
shaded lamps (the shades are to diffuse direct harsh lighting, don't go for one of
these and point it at yourself) and a
medusa to light up behind you would work just fine. Now you may be thinking why the hell do you wanna light up behind you and it's for the webcams sake actually. Contrasting lighting of brighter here and dark there actually make cameras work really hard to adapt to for lack of better wording. So you do actually want to light up the wall too to avoid that. You may want a small shaded desk lamp set on the floor as well if you plan to sit back to flash pussy or something too.
Now i'm just showing examples of the lights you wanna get with the links but what ones you pick out are up to you of course. Those are just showing the style. You wanna make sure about the wattage bulbs they can take as well as the type of bulbs they take. You want standard ones always whenever possible. A lot of Ikea lamps take special ones and they are a bitch to find. Especially if you want high or low wattage and LED. So standard is best cause you can get them anywhere and in LED. How high a wattage is important too as some are made to only take 40 watts and you may want 60 instead. Also you're gonna have to find if you want soft white, warm white, daylight and so on in a bulb choice as well and that just depends on your space and skin color too. So get several options and keep the receipt for returning the bulbs once you figure out which one is best for your situation.
Lastly I have no clue what kinda space you're working with so if you have more questions feel free to ask. This is just a general guideline.