As a former traininer, my first question would be do you need someone to show you exactly what to do in the gym? Or do you need that appointment with a trainer to keep you accountable? Plenty of my clients told me they could handle their workouts on their own, but the only reason they would be in the gym is because they had already paid for a session and i was waiting for them.
If you need to learn what to do to become self-sufficient in the gym, i would reccomend searching for a private trainer(not one working at a major gym chain). The name of the game at commercial gyms is client retention. So you'll be at the end of a full year of training, but your trainer may be holding back information or not actually showing you how to do things on your own in order to keep you as a client for the next year. Many trainers wouldnt even write you a specific program, they would just randomly select what you were doing that day to get a "good workout". At the gym i worked at, i was told to keep clients on simple machines for at least the first month, to "teach proper form". So that would be 10-12 sessions of standing beside you while you work a machine, which you could easily figure out on your own if you can read the labels. Working on machines is fine, but learning how to use freeweights, and more importantly learning why you're doing things/what muscles you should be working for each movement/how to keep progression and avoid plateaus is infinitely more important than sitting down at a machine and following the pictures on it. I eventually got pushed out of the gym because management realized that i was teaching my clients how to workout on their own, rather than withholding information to keep them under contract. My signup rate was super high, but my retention rate was awful because by the end of my clients contract, i was expecting them to be ready to go both physically and mentally to continue their workouts on their own.
I didnt really answer your question when it comes to cost, but from what i can remember there were certain promos you could get at different times, like "10 sessions for X dollars, 2 weeks for X dollars, etc." But again, with those sessions the main thing your average commercial trainer is going to do is try to show you how much you need them and how much you need to sign long term on. And as far as the training actually goes, trainers typically only really care about their long term clients. Being assigned a promo or trial client was always seen as a chore, since they knew it probably wouldnt result in a long term signing(and the commission that comes with it).
A final note, you stated your main goal is weight loss. With no background knowledge of you or your fitness past, your first steps are very easy. Simply moving more, and being more aware of what you're eating. If you're very overweight, start off with 10 minute walks every day. Turn that 10 into 15, that 15 into 20, and so on. Get in the habit of excersizing every day, and learn to not see it as a chore but as a part of your life going forward. As far as food goes, you can get super crazy and start weighing out your food and tracking everything, but that is hard to maintain even for a committed gym-goer. Stop drinking sugar, limit your treats as much as possible, and change up the volume of your meals. If you feel like a chicken breast and a cup of rice is not satisfying enough, find a vegetable that you enjoy eating with minimal seasoning/additives. A full bag of spinach with some balsamic and olive oil wont run you very many calories at all, but imagine eating an entire bag of spinach with your chicken and rice. You will have that same satisfying feeling of being full from the volume of veggies alone.
Good luck with your weight loss, and if you have any other questions on how to get started dont hesitate to shoot me a message.