I read your other recent posts about wanting to tear up your yard to landscape and also the basement moisture problem with the vinyl plank floors. I only have limited experience with this, so hopefully others will chime in. For a simple answer, I've heard most people now use a dimpled membrane, rather than tar/plastic sheeting. For new construction, but also seems ideal for your situation since you don't have to worry about the walls being clean. Did you plan on putting drain pipe at the footers as well? Does the water have somewhere to go?
I'd be cautious about having heavy equipment next to your foundation. I rented a backhoe on two occasions when I was excavating for a garage in a hillside--- one full size, the other smaller, and was quite the learning process. If you've never done this before, having a machine like that in close proximity to the structure is scary, for 1) the weight of the machine putting pressure against the foundation if the soil is soft and 2) in case you hit the controls in the wrong direction. Additionally, only the full size backhoe was able to dig at a 90 degree angle to the machine orientation, so its possible to back right up to the foundation wall and then dig along the sides. The smaller backhoe, a Terramite, could only swivel 60 degrees and with the stabilizers out, would have been difficult to dig along a wall.
Perhaps an option is to rent a saw and cut along the perimeter of the basement slab, then put in some gravel, drain pipe, and maybe sump pump if the water has nowhere to go? If you want to really keep moisture out, also put the dimpled membrane material against the interior foundation walls and let moisture drain down into your trench.
