What is the best starter kit for a hydroponic vegetable garden?

I don't know how ambitious your mom is but aerogarden is a very simple tabletop hydro setup that works really well. They start at about $50.I've grown herbs and lettuces and it gave me the confidence to build a 32 square foot aquaponics set up on my own.

The best hydroponics system for a beginner at the very entry level of hydroponic gardening would definitely be Emily's Garden by Hydrofarm. If you want to enjoy hydroponics at a more moderate level, then you should opt for the Microgarden or Turbogarden Ebb & Flow system. (only differences between micro and turbo are size/# of plants). Then, the more advanced hydroponic systems would be either the top feed drip or Aeroponics versions of the Turbogarden or Microgarden. The more advanced the system you use, the greater the likelihood that you will produce larger and more nutritious vegetables and fruit.