I would have just left a comment, but I don't have the reputation. I am an experienced amateur woodworker, but not a finish carpenter. If you try this, it's easy to exceed your skill quickly if something unexpected happens. Doors and windows are probably the most difficult finish carpentry tasks.
The person who suggested replacement with a pre-hung door probably has the best idea, as this requires less skill, though you will probably have to trim the bottom.
If you replace an existing door, you will need to mortise in the existing hinges. That will require either a router or skill with a chisel, or both, plus skill in marking the hinge locations. Chances are, the door will not be square in the frame on an old house as well, and you may need experience in scribing the new door to fit.
If you decide to go ahead, a solid core pine door might be a better starting point. The electric planer is the correct tool for removing small amounts of wood (1/16" at a time maximum) from the door edge. On real wood, it may cause some chipping of the end of the cut unless a scrap block is clamped on the end. For removing larger amounts, the tool of choice is a track saw, but this is primarily a professional tool. A circular saw held against a board or preferably an aluminum saw guide will do OK.
Score the edges of the cut with a knife before cutting to prevent any splintering of the wood when cutting or planing unless you use a track saw. Make a light knife cut followed by a heavy cut. Many people also apply blue tape on the cut line.
Of course, you can also do this with hand tools, which takes more skill as well to do a good job.
Keep in mind a table saw and chisel are likely the most dangerous power and hand tools, both can amputate fingers, hands, etc.
If you are new to an electric planer or circular saw, practice on a 2x4 first. A planer will take getting used to produce a straight edge. Coarse sandpaper is a slower but more forgiving option.
Another option is to consider repairing the existing door. Yes, the question is on replacement, but you may not have considered how easy a repair could be. It is possible to get specialty plywood to completely re-skin a slab door, though not usually at a big-box store. This needs to be very thin or the door will bind against the stop/jam if you add plywood on that side. You can also use bondo and/or spray foam to repair holes. This is a an approach that involves less skill, tools, and surprises. Your only tools would be a saw to cut the plywood or veneer to rough size, and a inexpensive palm router with a flush trim bit. You will also need contact cement.
