Welcome. I don’t have a lot of gear recommendations as I just bought what was available and stuck with it. It does what it is supposed to and I’m comfortable with it, but I have nothing to compare it with, so I can’t tell you if it’s better than what you plan to get or not. I do have a Henderson Thermoprene 5mm and am very comfortable in it.
When and if you move on to buying your own tanks, I recommend steel. You won’t need to wear as much lead, and you won’t have to worry about being more buoyant at the end of your dive than you are at the beginning.
I also recommend taking buoyancy as your first specialty class. You’ll feel so much more comfortable and in control in the water. My instructor actually recommends taking the buoyancy specialty before moving on to advanced. But I did it the same way you’re planning, ow, advanced, then specialties.
Good luck. Hope you find lots of buddies to dive with.