What type of hydroponic system is it? There are several methods. A picture would be helpful if there is already a system set up. If it's going to be indoors and there is not a significant amount of natural light, additional lighting will be necessary.
I currently have a small hydroponics system (two rows of 5ft spouting) that I built for my apartment last year. It has been running more or less continuously for 8-10 months and working quite well.
Most leafy greens/herbs are ideal for hydroponics because they don't need to go through a flowering/fruiting stage which is stressful for plants and often require an adjusted nutrient mix. Herbs also grow quickly and can be continuously harvest, and are also easily replaced if there are disease problems. The higher nutrient requirement for flowering and fruiting can actually kill some herbs and small seedlings. If feasible, separate reservoirs should be used for herbs vs fruit.
By far the most successful plant I have grown is kale. I've had two plants growing since the system began running and I harvest about a bag of kale per week. Since they don't branch out, you don't have to worry about them shading the surrounding plants more than 8" away. They are also quite hardy and have survived multiple drought-stresses (from a clogged/malfunctioning water pump) that killed all my other herbs, require almost no maintenance, and are prone to very few pests/diseases in hydroponics. Other successful herbs and greens have been parsley, cilantro, basil (sweet, thai, lemon), chives, arugula, and thyme.
Last month I designated an entire row to romaine lettuce which I have already been harvesting for a couple weeks; this is very easy to grow hydroponically and has a high yield.
I did have peppers growing for a time but they require some form of pollination, although shaking them can be enough. I'm not sure about your size restrictions but they may require pruning and staking. I recommend the small-fruited varieties such as many hot peppers (cayenne, thai, etc.; chiltepin has been my most successful pepper grown hydroponically and stays very bushy, so no staking) and possibly some of the small-fruited sweet peppers. Most of the varieties seemed to grow fine with the standard "balanced" nutrient mix that I use for herbs. I have seen other vegetables grown hydropinically: tomatoes, beans, chard... most garden vegetables that are not root crops.
I haven't grown flowers hydroponically yet but nasturtium should be a good bet; the leaves and flowers are also edible, and it will sprawl out instead of growing up too tall.
Posted by: Matt
Posted: July 24, 2015