Welcome to the Climber Club! As others have pointed out, trees with hard bark are more prone to slipping. Pine trees, some aspen, hemlock, soft maple, and black ash are great to start out on. You'll also find that some trees are noisier than others because platey bark tends to slough off in big chunks as you are climbing. Just take your time and you'll be fine. Because I'll climb any type of tree, I'll still occasionally have 'slippages' on hard bark...happened to me repeatedly on an oak this past weekend. After you've had it happen a couple of times, you'll learn to trust the equipment and won't get as excited when it slips a couple inches.
As long as you have your weight on it, it can't slip far before the teeth bite.
I think the biggest challenge for a lot of people starting out is learning how to adjust for tree taper. Just takes experience because every tree is different. Also, learning how to climb and descend quietly, and how to quietly pack/unpack the stand. I was on public land last night and some guy came in a few hundred yards from me...no big deal. Until it was time for him to descend. It sounded like a metal shop given the amount of racket (metal clanging and banging together) he made as he packed up his stand. I'm sure every deer within a quarter miles was on high alert...
Take your time and you'll be able to do it all blind folded with a little practice. And always wear that vest! Best investment you can make.