How did the appointment go? Hopefully it went well!
I've had good experiences in therapy and also not so good ones. One of my therapists just wasn't vibing with me I guess, I basically spent every session with her sitting in awkward silence and crying to myself while my therapist stared and said "aww, that's so sad." I have social anxiety disorder so that was the worst environment for me, not therapeutic at all. Plus that arrangement was very expensive.
My newest therapist is a lot better, she talks me through things and gives me actual advice. Personally, I need someone who does CBT. If you're not familiar with that, basically it's a exercise-style therapy. The idea is that your dysfunction is caused by cognitive distortions which come from core beliefs. The goal is to identify those distortions, come up with disputing questions and facts, and then practice dealing with them. I also do group sessions for exposure. This was all free through my school, and I'm thankful for it. I feel heard and like my therapist knows what to do. It's also focused on helping me function better, not just allowing me to rant.
As for suicidal talk, I would say try to be vague until you see how easily triggered your therapist is lol. Some are cruel and will try to section you for any hint of ideation. Others are more understanding. I've never had a problem revealing that I experience ideation, but I've also never attempted. It might be different if you have a history of attempts or self-harm. You can always just say that you don't feel comfortable discussing the details also, I always say that. I've never gone into details about the exact plan or thoughts I have, especially if they ask me about recent ideation.
Don't be afraid to interview your therapist -- a large part of the success of therapy involves the therapeutic relationship. If you can't trust your therapist, then you will gain nothing from therapy. Ask if they have experience with your condition, if they tend to be listeners, advice-givers, or have a more voice-of-reason approach. You can even ask their opinion on religion, politics, and recovery topics and see if there are any glaring differences on that front. Sometimes a therapist will ask something like "why is it important that you know this about me?" usually they're just trying to get a sense of you since this can reveal fears of judgement, sense of safety, or trust issues.
Don't be afraid to "fire" your therapist if you don't get along, don't wait til you're months along and feel obligated to stick with them. Most good therapists will be happy to give a referral to a colleage that may be more experienced with your situation, or simply more in line with your expectations.
Good luck! Therapy can be completely life-changing for some people, hopefully you're one of them!