Nutrient pH 6.0-6.7 EC - 1.4-1.8 PPM 980-1260
Most onion seeds germinate in about a 6 - 10 days in temperatures of 65-70 degrees F. You should expect to harvest your onions 3- 4 months after starting from seed. Starting from sets, expect to harvest in about 80-90 days.
It is best that you have no nutrients in the water for the first few days that you place the seedlings in. By starving the onions in the formulative days the roots are forced to grow strong and vigorous in search of nutrients. When you do incorporate nutrients to their regimen, they will have a stable root base to absorb those nutrients and optimize growth.
With Onions, care should be taken to use a balanced nutrient solution. Too much nitrogen will create excessive foliage at the expense of the Onion bulb itself. 
Too little nitrogen will lead to a deficiency characterized by reduced growth and stamina. Follow directions on the packaging of the nutrient supplier. Monitoring and maintaining pH and Electrical Conductivity are important in ensuring the proper synthesis of available nutrients.
See - TDS in Hydroponics
Checking pH. After adding the nutrients, wait at least an hour prior to checking pH.
Aeration. You should aerate the solution continuously not only to maintain hydroponic nutrients and discourage anaerobic bacteria bu to oxygenate the roots as well.
Chlorinated Water. if you are using Chlorinated tap water in your hydroponic set up, it should be allowed to sit for 48-72 hours in order to dissipate the chlorine.
Nutrient solution should be one designated for root vegetables. General purpose nutrients will suffice, but one specifically designed for root crops is best.
In nature Onions do best in full sun. In a hydroponic system indoors they need about 12 hours of light daily, this varies depending on the variety . Short day varieties will get by on slightly less - see Onion Varieties.
If growing outside - Onions themselves in nature can tolerate some frost and snow, but be aware that if your solution freezes, kiss them goodbye. The optimal temperature range for Onions is 55 to 75 degrees Fahrenheit. When grown out of this temperature range they sometimes bolt to seed. Bolting Onions should be harvested ASAP.
An ultra simplified startup system for Onions can be made with some polystyrene, some flower pots with an adequate depth and soilless growing medium. They can even be grown on a window sill.
For a reservoir, a Tupperware or storage plastic bin will suffice, depending on how many Onions you plan to grow. Your reservoir should be a minimum of 6-8 inches deep.
Trim the styrene to fit within the reservoir, allowing for a small clearance around the circumference of the styrene or Styrofoam. The styrene will float to the surface of the solution.
Cut holes through the styrene to allow only the botton of your pot to sit in the hole. Pots are narrower at the base, so the top will be above water.
Insert the pots in the holes and fill them with a lightweight medium. Perlite Vermiculite blend, I feel, is best. Your onions will grow in this medium so long as they are provided with the adeqaute nutrients
Green onions can be harvested in as little as 3 weeks using this system. The solution should be replaced monthly.