FWIW, Boby By You or even You Are Your Own Gym are another good ones for strength. New Rules For Lifting rocks, it really does. I love it (all three really.)
Circuit Training and HIIT have been proven to be beneficial, he is trying to get you to focus on muscle building, which I guess is fine given he is a personal trainer, but really, he needs to back off about the don't encourage it...because really, most experts encourage you to do anything you will do, and Circuit and HIIT tend to be thinks most people go towards due to the high calories and low sculpting in short time.
I think you'll love NRFLFW. I love it...I used to think 10 pound weights were heavy. Now, if it is less than 20, I feel it is a joke.
And I really do recommend BBY or YAYOG as well. You said you can't do a single push up...those two books are about body lifting (which is more hard than I ever realized) and by the end, you'll be doing some pushups! I just started one and I was only able to do 35 at first. A little over a week in and I am able to do 60 now. It builds crazy strength, crazy quick.