You're looking for that exact answer. You want me to say, "it's the 10 minute timeframe," but it's not that easy. It depends on what kind of a system you are trading. After you've defined that, the right timeframe becomes obvious.
For example, if your trading a system that doesn't seem to care about the price (yes, such systems exist), very fast timeframes would be appropriate (somewhere in the range of 3 to 5 minute bars). Realize that the faster the timeframe the more chaotic. In fact, there is hardly any order on the really fast bars. It's true chaos.
So, if you were trading a grid trading system or a hedging system, then a really fast timeframe is okay. You don't really care where the price is going. You're not going to be doing any technical analysis on it.
However, if you're trading any kind of system that uses any kind of technical analysis, you definitely want to use a slower timeframe. You need to give the system something to sink its teeth into. The 30 minute chart seems to be a good choice.
Depending on the system, you may need to go larger or smaller. For example, you can use Fibonacci retracements on a 15 minute chart.
If someone were to come up to me and put a gun to my head and ask what is the best timeframe for day trading, I'd have to say that I'd want a 5 minute chart and a 30 minute chart open side-by-side. (Then I'd disarm him and give him the business ;-)