Hi Hyacinth! I think your decision to look for a PT is a good one but you are exactly right that he/she needs to be the right kind of trainer!
May I refer you to something I posted a few years back about finding the right trainer?
How To Pick A Personal Trainer My best ideas are in that post.
Let me emphasize that YOU are the consumer and YOU get to pick your trainer, not the gym. Gyms and trainers are hurting financially right now -- you're the one with the money and trust me, a good gym will bend over backwards to make you happy and satisfied. Do not accept a trainer who is "assigned" to you! That's baloney. If you're going to work through a gym, call and ask to speak to the head trainer. Make your needs and preferences known. If you prefer a female trainer, say so. Ask for a free session so you can evaluate the trainer who they recommend. And speak up if that person isn't a good fit for you!
Yes, there are independent PTs who are not associated with gyms. Some have studios and some will come to your home. I'm not familiar with your area but I imagine you can find some names through google or referrals from friends. Again, YOU are the boss! Interview them and do not hesitate to walk away if they can't meet your needs.
Good luck, be assertive, and I'm sure you can find someone to help you on your journey.