Congrats, im sure you will enjoy it. I will give you some input in two ways, listing why i left my previous trainer and why i now see my current trainer 6 times a week without any regret:
Old trainer (why it didnt work)
a) She constantly spoke to me about her personal life and her challenges, drove me insane
b) She constantly spoke about her financial challenges which also drove me insane
c) She didn't keep track of anything
d) She didnt push me, the sessions felt like something i could do without spending a large sum of money every month
e) she only measured my weight as a progression measurement.... pfft
f) I packed on muscle, but never really lost fat
New trainer (and why its working)
a) He kicks my ass past what i believe my limits are every week (and has done so for a long time). One of the core reasons i will stay with him is that i know without him there i wouldn't be able to push myself that hard. Initially i was wondering if i should stay with him because of this (And it felt like shit puking, lol), but after two weeks I loved it
b) He can actually tell when im not eating what i should based on my energy levels in the gym, this really helped me sort out my eating. He even started phoning me at work asking me "what are you having for lunch"... was funny. It forced me to go from 1400 cals a day to 2600 cals a day
c) He changes my routine alot, which makes it feel "new" every two/three weeks
d) He keeps track of progress and makes sure the intensity goes up every second week.
e) He introduced me to some of his other clients who are like minded, i believe this is great, because when i go to gym now we are all motivating each other, etc
f) Measurements are now done on body fat and body measurements which is great
g) packed on more muscle and my body fat dropped exceptionally fast
h) i feel "safe" with him around. when i bench a number which i think would kill me i know he has my back.
I think everyone is different and everyone requires a different approach. However, i believe that a personal trainer needs to push their clients beyond what the client "believes" is possible... My mother and sister also use my trainer now, he really pushes them too, and as lazy as my sister is, she loves it.
Again, i see the new trainer for 6 days a week, and its fun. Would also recommend not taking clients for less than 3 days a week.
edit: oh and he is a bitch for the right form "the previous one wasn't". Not just "telling" me, but showing me or manipulating my movements physically when i struggle keeping it.
That will work in your favor for the PT. 
