I read the OP but I'm not sure how well the full body workout outlined in it would work out for me.
First thing I noticed is it recommends Squats every single time. I don't want it to sound like a cop-out but from past experience Squats do a hell of number on your Quads - I live in New York City, I'm not sure I can manage that pain in my thighs with the shear amount of stairs I climb every single day (in and out of the subway system and an immense amount of walking since I don't have a car). I used to do workouts when I started college about 7 years ago and just getting around the campus in super flat Florida after a few sets of squats was pretty tough and I drove almost everywhere. If I do squats it would have to be taken into strong consideration.
Second thing is I have no spotter and I can't afford a personal trainer. I have access to a lot of machines but I'm not too keen on trying something like a Deadlift for fear of hurting my back (is there deadlift machines??) and the Bench Presses would have to be all weight-selector machine assisted. I also highly doubt I can do pull-ups... I'll give it a shot but if I'm struggling with 15lbs I have a feeling it would be a while before I can lift my own body weight that high and hold it there for any significant amount of time - let alone doing it 45 times like the OP suggests.
Squats only hurt the first week, maybe two at most. I squat three times a week and never suffer from it. If you do 3x5 squats you will be fine once your body is used to doing more than sitting on its ass. The whole program isnt designed to wreck you every workout.
Those numbers of pull-ups arent something you will reach for a while, so dont worry about it. Do 3 sets of whatever you can, or, in case you cant do one, do 3 sets of negative pullups. Or you can even do a wide-grip lat pulldown, although it is a poor substitute, but still better than nothing.
You can replace the barbell benchpress with dumbbells. Thats just fine, and might make you feel a bit more secure.
And no, you wont hurt your back doing deadlifts
if you take a few minutes to learn how to do them. Thats why you start at a really low weight and gradually ramp it up. That gives you plenty of time to learn how to do them.
In the end you can complain and make excuses, but it simply is a matter of hardening the fuck up. You want to become stronger then you got to be willing to take the pain.