Reddit mentions of LimoStudio 43" Photography Photo Video Studio Lighting Disc Reflector, 5-in-1, 5 Colors, Black, White, Gold, Silver, Translucent, AGG808

Reflector, $17, free shipping with Prime

Things to Google and read about in depth:

• Color temperature: it sounds like you're using a warm incandescent bulb now and you probably had a cooler, bluer "daylight" temperature bulb before
  
  
• Manual white balance correction: depending on which camera you're using, there should be either a specific color temperature (in º Kelvin) you can set, or a basic description like tungsten (very orange street lights and incandescent bulbs), full sunlight, florescent lighting (usually has a green cast in photos), cloudy day and shade (usually much more blue tones). There's an auto setting that usually does an okay job. Then finally you manually make a precise adjustment by taking a single shot of a white piece of paper and tell the camera "this should look white" then it'll calibrate based off of that.
  
  
• Shooting raw & correcting in post: When you shoot JPEGs, color information is baked into pixel groups during the compression process. You can adjust the color later but you lose some image quality. If you shoot raw instead of JPEG, the color information is stored differently and you can do a lot of color interpreting without degrading quality. It may be no big deal, but it is a great benefit of raw photo development that shoe balance can be done entirely accurately later with no image quality loss.
  
  
• Hard vs. Soft light: A single bulb provides hard light because it's a small point of light and produces sharp, distinct shadows. If you pour a lamp shade over a bulbit "softens the light" by making the illumination source more broad, this shadows are softer and less pronounced. It's eat to make good quality light modifiers by bouncing light of of a broad surface like an adjacent wall or ceiling, or off of a reflector or a softbox of some kind (the grid helps control light from spilling of your subject but that mint not be necessary). Even a lampshade can help here.
  
  
• DIY product lighting: there are dozens if not hundreds of great articles and YouTube videos on creating exactly what you're trying to set up for very little investment. There are inexpensive products on Amazon, and there are cheap ways to make a lighting rig with materials you probably have laying around the house
  
  Good luck!

If you have not done lighting before, you should really practice first, and you should simply buy before renting. If you don't know how to use basic cheap equipment, you'll have even more problems trying to use higher end equipment.

I would buy instead of rent, it's about the same price and if you learn how to use it properly you'll get the same results. The reason pro equipment costs a lot is not because it makes your photos better, it's because it's more reliable, quick, etc. Lots of pros don't always use pro equipment.

Neewer TT560 - $40

Flash stand with umbrella - $33

43" reflector - $13

Total: 86

Stand the model in front of a white background, put the Flash and umbrella at a 45 degree angle from the subject, hold the reflector on the opposite site to use as a fill. Use photoshop to turn the background pure white.

If you want to go super budget, buy 3 canlights from home depot ($7 each), buy 3 150w equivalent dailight CFL bulbs ($13 each), and a piece of white foamcore board ($1) for a total of about $70 depending on the pricing close to you. Use one can light as a key, use the foamcore board as a fill, use a 2nd can light as a background light, and the third as a backlight for the subject. You will of course need something to clamp the lights on. If you are doing full body shots you can use a white shower curtain as a diffuser for the key canlight.

Here's a lighting tutorial that you can use to get some ideas too. This site has a lot of tutorials you can check out. Ignore the pro equipment, it can almost all be swapped with DIY or cheap equipment.

Agreed, OP should get one of these