Hi OP - congrats on getting yourself to the gym, I hope you're already starting to feel the benefits.
You've several options, and there's no need to rush to the free weights until you feel comfortable, and you've been given some guidance on how to use them properly to avoid injury!
As you're fairly new to the gym, I'd start off doing three full body weights sessions a week. Something along the lines of:
10 min cardio warm up
Four sets of 12 on the following:
Leg press OR leg curl and hamstring curl
Lat pulldown OR sit down row OR back fly
Chest press OR chest fly
Shoulder press
20 mins of cardio
You could alternate the machines each time - so one day your leg exercises could be leg press, your chest chest press, the next the curls and the flies etc.
Try to space out your sessions. If you're going on a fourth day, you could do a full cardio session as you've been doing, or do some abs, body weight exercises, biceps and triceps alongside the cardio too.
The most important thing is to find what works for you, and what you enjoy.
Good luck!