Central Athlete on YouTube has really clear videos of different weight lifting exercises.
Rowing on a machine is a great cross between cardio and strength, as a transition. Get one of the trainers to show you the right technique though - your knees should not get in your way at any point! It works arms, legs, core, back, so it covers all the main muscle groups. Stroke rate about 26/min, focus on the power as you pull through
Machines are good to start with if you don't have much strength as they usually have a diagram of what to do, or at least a label of what they are, so you could Google how to use them. Plus, you're much less likely to injure yourself with bad form on a machine.
Dumbbells are your friend as well - start nice and light, so you won't hurt yourself, but the extra muscles you're using to create stability are helpful and will help you eventually transition to free weights.
I'd recommend leaving barbells for now until you have more strength and confidence, or until you can get a trainer to show you correct technique - certain things it's important to have the right form or you can damage yourself.
Aim for 3 sets of 8-12 reps for each exercise you do - but if you can't do that many, no worries, just do what you can. The last couple of each set should be a bit of a struggle, but achievable - that's how you calibrate it to be about the right weight for you.
I'd suggest picking 2 exercises from each of the 3 sections below (so 6 exercises total) per gym session. If that's too many, do what you can and build it up over time.
Some good things to start with:
Legs:
Squats with bodyweight, or a kettle bell if you can.
Lunges with bodyweight, or with dumbbells if you can (many variations, look some up!)
Hamstring curls
Leg extensions
Leg press
Hip abduction and hip adduction
Core:
Russian twists (can add a kettle bell as you progress)
Planks (front, side, walking, mountain climbers)
Hip thrusts (bodyweight, then kettle bell then barbell)
Pallof press
Leg raises.
Single or double kettle bell farmers walk
Arms:
Shoulder press
Lateral raise
Lat pulldown
Single or double arm rows with dumbbells
Tricep press
Chest press
Hammer (bicep) curl
Floor press
Arnold press
Good luck!
You'll likely find it hard to start with, but stick with it and you'll feel better and start seeing the gains pretty fast if you're consistent.