Lyn,
I was very much into weight training before this arthritis ravaged my hip. I tended to focus on the dead lift and standing overhead press, along with squats and other free weight exercises. I did spend a few years in a commercial gym back in the day.
I'm 9 weeks post-op, and just returning to some light exercises. My PT suggested keeping weights at 25# or less for starters, and no more than 50 total reps for any exercise. She said that all upper body exercises are OK, as well as light squats using a dumb bell or kettlebell.
My OS is a bodybuilder so he has some practical experience. He said there's a trade off between weight lifted and prosthesis longevity. Stressing the implant with heavy weights and high repetitions will result in shorter implant life.
He also said to avoid stances that involve lateral or backward movement of the affected leg, especially in combination with external rotation of the hip, in other words, turning the toes outward. So you'd want to avoid the so-called sumo stance for the dead lift. (I'd think that you should avoid the dead lift altogether since it places huge stress on the hip joints). Lunges might be suspect. I had an anterior surgery, so these restrictions might not apply if you had a different approach. Of course you should check with your provider about your particular restrictions. Consult with a provider who has personal weight lifting experience if possible.
Finally, my OS said that most exercise machines are safe, as long as no stress is placed directly on the hip. Machines usually have seats and sometimes restraining devices meant to isolate specific muscle groups. This protects other muscle groups, which is a good thing when using the machines for rehab purposes and when trying to develop specific muscles.
Hope this isn't too technical, and that it's somewhat helpful. Good luck!