Most kites that are rated to fly in 1-2mph will break in winds over 10mph, and they are too fast & light to do much with once the wind is over 5-6mph. If you're looking for an all-around kite to fly in 3-15 mph, the Prism Zephyr, Blue Moon Exile, or Skyburner Widow Maker would be great choices. The Zephyr is rated as an UL, but that is highly debated, a number of people can't get it to fly in low winds, but the other two are standards that will fly easily in less than 5mph of wind.
You won't be able to find the Exile or Widow Maker new (more than likely), but they do come up on the used market at a price comparable to the Prism Zephyr. Along those lines, a Prism Quantum Pro is rated 2-20mph, it is all the kite that most would ever need, but you will probably have to settle for used. If price isn't a concern, Lam's kites have a wide wind range, especially the kites that he rates as 'light'. I had a Sea Devil 'light' that would fly easily in 2mph of wind, and not be too out of control in 10mph+.