As Tom mentions, if the doors are precut for knobsets, absolutely....cut off the hinge side. If you've bought slabs without knob & hinge mortises, you still should cut on the hinge side; the strike side of a slab door will sometimes already have a beveled strike edge, even if it doesn't have mortises.
Before cutting, I would clamp a straightedge to the door just barely INSIDE of your cut line, and score through the skin with a utility knife; this will help prevent chipping and splintering of the face side as your sawblade is coming through, and disappears when you slightly round the edges in sanding. As to blade depth, I would set the blade to near minimum needed. It's also handy to clamp a straightedge or good, straight 1X6 on the door as a guide for your saw; just set it back from where you want to cut by the width of the saw shoe to the side of the blade. Just be sure it is clamped solidly and won't bow as you cut.
About power planes; this is a tool I personally wouldn't do a door without. You can use your skilsaw to remove large amounts, then use the planer to do your final and a clean-up pass, removing as much as 1/8", to barely skimming the surface, one pass at a time. A planer will give you a nice, smooth factory-finish edge. It's a must-have tool, especially when it comes to fitting new doors to pre-existing jambs.
These are also handy for scribe-fitting woodwork to match slight curves or uneven walls. Many, many uses for this tool.