Probably depends upon the type of studies done in this first phase.

1 With a small effect size, if the smallness is due to inherent variability of the responses, the web is preferred for the gain in statistical power.  If the smallness is due to sensitivity to conditions, the lab is preferred. 2 if have resources for a real proportional sample – use traditional methods (phone, mail, etc) if not, the web will probably still be more representative than a college sample but both have significant biases 2 If the validity is driven by more varied subject populations – web;  if by more varied conditions - lab

Unless all other factors are equal