Addressing the haggis sounds great.
I was taught how to use a multi-gym as part of my PE at school when I was 15. It was one of the most enlightened PE courses I've ever come across, because it was genuinely useful.
Perhaps what you need is low impact cardio-vascular exercise and some 'core'. Bit of swimming will be good for this. The rowing machine good too. The spinning bikes might be fun and familiar, but don't puke your guts up. Those three are all cardio activities. Perhaps then some gentle free weights exercises, a small weight in each hand. That could be the most satisfying part of the session.
Those big machines with the captive weights attached to pulleys are probably the least useful machines in a gym because they work very few muscles and the fitness they produce is not very usable in the real world. But they're satisfying to use, and they're popular because they're safe, with the weights being captive, so they need minimal teaching to get the user started.
Anyway, you'd start any session with cardio and stretches and only then attempt weights (if you're gonna attempt weights). You'd finish with more stretches. Don't skip the stretches.
A lot of personal trainers in gyms aren't paid by the gym, instead they upsell their services to members, and so there's an incentive to advise 'supervision intensive' activity. So, pinch of salt with their advice of activity. Their main function, for the gym, is to deliver safety briefings so the gym doesn't get sued by the punters.
Honestly, I think I'd walk around when the place is busy and see what I fancied trying, then figure out where that activity would fit within the basic sequence. The basic sequence is 'cardio - stretches - weights - stretches'. After that, I'd try ignore the other people in the gym, because gym people.
