The answer is that it all depends.
Assuming it is a liquid stock, I would buy at market. The spread should not be too wide in a liquid stock and I will get set for sure. The best stocks to buy are the strong ones and they are the ones I tend to miss with limit orders. However, your trading plan may be quite different to mine.
It also depends on how much time you have. If you can monitor it closely with a "straight through" Internet broker, you could try placing a limit order in the spread and see if you get done. If you are able to watch it closely, you can see if the stock is moving away from you and quickly adjust your order.
It also depends on the time frame you are trading and on your trading plan. If you are a position trader like me, a cent or two is not critical. However, if you are a scalper or a day trader, it will be absolutely critical. So a limit order would be mandatory in those situations.
If you use a live broker on a telephone, rather than the Internet you have a lot more options, because you can get the broker to monitor and manage your order.
Assuming the stock is not very liquid or has a large spread, I usually use a limit order and am prepared to miss out sometimes. New opportunities come along all the time.
Finally, I must stress that buying the breakout is only one possible tactic. I tend to put part of my position on because I do not want to miss out on the really good ones that take off. However, I will build my position on a subsequent correction, which happens most of the time.