I rewired hundreds of HUD homes back in the '70s. I've experienced just about every type of construction known. Your home is the easiest to rewire because of the unfinished basement. The only hard part are switch legs.
All stick-built homes have a hollow space between interior walls. You just have to know where to drill to get a wire to where you want an outlet.
Envision your interior wall with a base plate made of a 2 x 4 on the flat. The studs are 16" on center so you have a space you need to hit from below that's 14 1/2" long by 3 1/2" wide. That's your target. Studs can be located by tapping on the wall or using a stud-finder. There is no need to remove the base molding. I've never had to do that. What you can remove is the shoe molding to drive long nail right below where you want an outlet or switch. It's best to pick a location where one wire will feed an outlet on either side of the wall.
Once you drive the nail most of the way in go in the basement and find the shiny nail sticking through the floor, into the basement. If you measure about 2 1/2" from that nail and drill up you will be in the hollow space of that wall. If you're unclear of the orientation of the wall above drive a nail on the other side of the wall and split the difference between them to center the drill on the space above.
I had a journeyman that I worked under that wished he had driven the second nail as he found a shiny nail, but it was the wrong one. He ended up drilling into the lowest drawer of a dresser. When he figured out what he had done he opened the bottom drawer to find a massive circle of twisted dress shirts. I had to

.
Outlets on the outside walls are a little tougher to do, requiring an 18" ship auger. That's because the trusses sit on top of the concrete or block wall, meaning that the outside wall you want to get into is about 8 inches away, requiring an angled hole. In this case you want to drive a nail at the baseboard again. This will mark where the drill bit will have to start to get into the wall space above when drilled at a 45° angle to clear the foundation. You'll be drilling up through a basic floor plank of 3/4" and a 2 x 4 which is over an inch and a half on an old house. By the time you penetrate the top of the base plate the hole will be at the rear of the space.
Finding walls in the attic is easy as the trusses sit directly on the top plates, made of 2 2x4 on the flat. The lower layer is so you can build a complete wall and the second is to give it strength and to overlap onto adjacent walls to tie everything together.
Since the attic beams sit on these walls they are clearly visible under the insulation. You can locate where you want to drill down by simple measuring off know corners below. The outside walls near the eaves are often difficult to drill on low-pitched walls but can be drilled straight down with a right-angle drill and stubby ship auger with a screw feed.
Just remember to give all your wiring 2" of mechanical protection. Simple stapling at long runs and direction changes should suffice. I could draw you pictures if you need them.
Edit, on the subject of lathe plaster. I would have loved to have had today's rotary tools. Hand saws made quite a bit of work for the plasterers that followed us. Done properly the rotary tool should eliminate most repairs.