In exploratory work I prefer to have a higher rate of 'false positives' ('higher' Type I error rate) that can be ruled out later in confirmatory work. So, for example, use p=0.10 instead of p=0.05 (or balance with power in some way). You're asking the question What could be important? If you use a p value that's too small you may miss a real effect.
In confirmatory work you'd like to answer the question Are we sure this is real? and so you'd be better off using smaller Type I error rates (p=0.01 maybe). More n needed, but less factors you're analyzing.