Well here's thing thing. Most of the inuries associated with free weights come with either the very advanced using very heavy weights (plus with a history of imbalanced routines and perhaps not so good form) or over the course of many years when overuse builds up and basically a theshold is reached. Lots of trainers scare people about free weights and tell them machines are "safer". But they are wrong and they don't really understand where the majority of injuries come from.
Actually there is a very good thread on this so I will point you to that. But the thing about machines is they can LEAD to injuries and multiple ways. Especially problematic is this false sense of security people get from machines. They think that machines will "get them ready" for free weights. They DO NOT. Much more likely is that people will go to free weights right off the bat that are too heavy becasue they think that the 'strength' they gained on machines has prepared them. So they pick up a heavy dumbell and pull something just like that. Or EVEN they pick up a light weight but have used machines so long it has resulted in patter overload and all sorts of overuse of certain muscles because the unnatural plane of motion, etc...and they end up with an inury from free weights they never would have gotten in the first place if they had used free weights and skipped machines. I could go on and on but I think you get the picture
You could simply replace leg press, leg extensions and leg curls with the aforementioned single leg squat variation done with dumbells and you could do dumbell deadlfits as well to get used to it before you move on to a straight bar.
Also, for God's sake get off the low back machine. Instead learn how to do bodyweight back extensions, or reverse hyperextensions, and do planks, side planks, etc.
I'll get back to you later.
Edit* I just saw atclarkson's post. He is on top of things. Why didn't you list his suggestions?
. Goblet squats are a good idea. DB bench press. Everything so much better.
And for my usual reminder. I think EVERYONE should be doing some type of single leg squat all the time or most of the time. This is not a girl thing