Most rentals are just that, rentals. Beat up, dull edges, etc etc.
The custom is a directional freestyle board. Basically it's got a directional core, very slight directional shape, but it's still got plenty of flex and pop for freestyle, and an almost centered stance. With the size you choose, as schmitty said, you are fine. The board will feel alittle softer for you than someone who is 150# though. Keep in mind the Custom isn't a super stiff freeride deck, Burton makes the Custom X for that. The custom is just a good at everything, all mountain board.
As for your stance, you've got your own board now
Play around with your stance and make it comfortable for YOU! That's one of the huge perks to owning a board as a beginner.
The two things you are going to want to set are the stance width, and binding angles.
Stance width is the distance between the center of the binding plates. If you installed your bindings in the holes that are marked as the 'reference marks' you're probably at around 20-21". This is fine for most, but if you're a little taller, you may like something around 22-23 for the additional stability. If you widen your stance, do it equal with the front and back binding so that your stance stays centered over the sidecut. Wider = more stability at the cost of easier turn intiation. Narrower is visa versa.
Secondly you want to you look at your binding angles, most boards that you rent are probably set at something like 15* Front/ -3* Back. Which is actually a pretty good stance to start with for someone who just freerides. If you ever plan on riding switch much, you might want to duck the back foot out a bit more, and prefer something like -6 or -9* for the back binding. It's all up to you to decide what feels right
Other than that, as schmitty said, it just takes time to get used to your new board.
I rode a Never Summer for most of the year, and I couldn't resit a killer deal on custom 162 about a month ago. It took me a couple runs to get used to how the board felt, but after that I love it. The trouble is, I feel like I'm cheating on my never summer, cause I love it too.......but that's another story