Window Farming: Do it yourself veggie garden in your window
npr.org
npr.org
Get 2 of each starter plant you want, get used to the idea of death. I see many first time gardeners get overly emotional about a couple small plants, this amplifies the stress of failure too much.
Start with herbs. Things like oregano and basil give a huge flavor/effort payoff compared to fussy plants like tomatoes. They are very hearty and a little goes a long way.
After you get fresh herbs on hand for your kitchen, you won't ever want to go back.
http://earthtainer.tomatofest.com/
Time will tell if it works well.
</parody> Seriously, some hardware gizmo that automates care and data-logging. I can totally see that done with those new cheap programmable MCU/SoC boards, like Arduino.
Edit: Even better (phone control, twitter notification, etc):