Frequency depends on the individual. I started out once per week, but once my therapist and I realized I had done so much research th at I knew the answers to all of the questions normally asked we switched to once every 4-6 weeks. I'm sure once hormones start making significant changes and I get closer to full time the frequency will go back up.
Also if you have other things to talk about, other than gender identity/transition, that would increase the frequency too.
My therapist is $150 per 50 minutes so your prices look about right. My insurance covers 50%, but if your insurance doesn't cover it many therapists have a lower income/uninsured rate available. (Usually $60-$90)