I did a lot of them growing up in father's business. None since, but I would have no fear of the work. K and T can be generally good quality.
Change the service and run new romex to all the heavy loads and appliances. Don't leave a washer, fridge, or microwave on the old when you are done. Knob and tube is fine for what it was designed for in 1930 when the only loads were a few incandescent lamps and one or two small motors. Take the load off the K and T and leave it in place where it is covered in the walls for existing lights and a few convenience outlet loads. Check with the inspector first for an approved method of transitioning from romex to K and T in the basement at the point where it goes up in the wall. If they are insulating the walls or ceilings, imo, K and T is not rated for insulation contact and would be coming out. Remove it from where it is accessible and replace with romex.
I would GFI at the panel and not try to change devices or concealed splices. As soon as you commit to changing all the devices and open the boxes, you'll probably find the boxes are too small and everything is coming out. I would change devices individually when they fail. K and T with soldered splices can last forever and is good quality. Twist and tape splices are already in the process of failing.