Fix workout for newbie with lower back pain

I am pretty new to gym life and try and get there 3 to 4 times a week, I am kind of lost by the amount of programs and videos and methods that get posted. I have a lower back issue that I am doing PT and seeing a chiropractor for, but it's causing a sciatic nerve issue that gives me random shooting pain in my leg. So I have been told no hinge movements :-(

I do a lot of cardio as it's easy, and somehow, when I run, the pain in my leg goes away. I am eating better for weight loss, but I feel I have no real idea what i am doing at the gym. trying to find a trainer or a gym buddy to help.

Could someone help me with a newbie-friendly program and also explain if I need to be progressive lifting or lifting to I fail.

The Gym is small, and I spend most of my time in the machine room, but these are the machines that I am normally on. I am slowly moving up in weight once things start to become easier.

Threadmill C25 (Week 6) (30 minutes of processive running)

Elliptical 25 Elliptical (25min of random hills with push pull arm workout)

Machine Chest Press
105lbs X 12 reps 3 times with 30-second break between reps
115lb X 12 reps 2 times with 30-second break between reps

Machine Triceps Pushdown
130lb x 12 reps 2 times with 30-second break between reps
140lb x 12 reps with 30-second break between reps
150lb x 12 reps with 30-second break between reps
160lb x 12 reps 2 times with 30-second break between reps

Machine seated Row
100lbs x 12 reps 3 times with 30-second break between reps
120lbs x 12 reps 2 times with 30-second break between reps

Machine Bicep Curl
60lbs x 12 4 times with30 second break between reps

Machine Front lateral pull down
120lb x 12 reps 2 times with 30-second break between reps
130lb x 12 reps

TDLR
Looking for a newbie plan without any hinge lifts due to back pain, looking for guidance on the method to gain strength.