My father is asking me to do portraits of the family, and I need help finding what type of lighting equipment I need for this task. Soft boxes, umbrellas, etc.? Which would be best in my case, but not too expensive?
If you are not experienced in using artificial light for shooting portraits, you will want to start out using incandescent lamps so you can "see" how you are lighting them.
The best for the price may be this "kit" http://www.bhphotovideo.com/c/product/285789-REG/Lowel_GO_95LBZ_TO_GO_95_Kit.html
You will also need a background stand like this one. http://www.bhphotovideo.com/c/product/395974-REG/Savage_6203750_Background_Port_A_Stand_Travel_Case_.html

If you are not experienced in using artificial light for shooting portraits, you will want to start out using incandescent lamps so you can "see" how you are lighting them.
The best for the price may be this "kit" http://www.bhphotovideo.com/c/.....5_Kit.html
You will also need a background stand like this one. http://www.bhphotovideo.com/c/.....Case_.html
References :
Fashion and glamour photographer