Hi Jack,
Lucky for you, one of the most effective lights for what you want to do is also one of the most cost effective options for indoor growing! The Jump Start T5 Grow Light System will provide all the light that you need for growing flowers and herbs. It comes with a high output T5 fluorescent bulb, a light fixture that plugs into a normal wall outlet, and a stand which allows you to raise the light up as the plants grow.
The T5 bulb is designed with enough output to supply plants with adequate light for as little as 12 hours per day (the minimum light requirement for most plants). However, no matter the bulb you decide to use, 12 hours will not be enough light for pre-flowering plant growth phases. You will need to have the light on for 14 to 18 hours per day until your plants begin to flower. If you want to, you can induce flowering by providing just 12 hours of light later on, but doing so is not necessary for plants to flower, it is more or less like a trigger. That being said, an HPS bulb or a bulb which provides more colors on the red spectrum will boost the flowering of any plant.
The space you are working with is not large enough to support the amount of light you would receive from an HPS bulb and ballast system (not to mention the expense), the T5 system accepts warm (red) fluorescent bulbs meant for flowering. These bulbs are sold separately but are only slightly more expensive than the standard replacement bulbs (the one that comes with the T5 system).
For your set up I would recommend the 4 foot Jump Start T5 System, a timer for consistent light duration, a Hot House Kit (everything you need for seed starting besides potting soil), and a 4 foot T5 warm bulb for flowering later on. Below are links to those products.
https://www.planetnatural.com/product/jump-start-light-system/
https://www.planetnatural.com/product/grow-light-timer/
https://www.planetnatural.com/product/hot-house-with-heated-mat/
https://www.planetnatural.com/product/t5-bulbs/
Good luck!