What's important in selection of a suitable microscope objective (regular bottom thickness chips)?

A inverted miscope is recommend, as most surface for observation is on the bottom (non-inlet side).
The objective working distance is a critical parameter for selection of an objective.  Most default objectives are indented for a #1.5 cover slip which is only 170µm thick, where the thickness below channel is mostly in the range of 400-900µm.   
Those objectives with longer working distance are often called non-coverglass objectives.
Where possible we would recommend to work dry. In most cases it should be possible to use the channel edge or other well defined point  as reference for manual size corrections, this would reduce the need for corrections by the objective.