Does knitting needle material make a difference in knitting?
This question cannot really be answered.  And the answer to why is both easy and complex.
TL;DR: Start with one kind of needles, it doesn't really matter which kind, preferably one you can borrow, or some cheap ones, and decide after that if it feels right or not.
Like someone already said, knitting needles are made of many different materials, the most common are wood/bamboo, metal and plastic.  But you will find other kinds if you look, like carbon, ivory, bone...
Anyway…

Wood/bamboo needles are usually less smooth and slick, it means that the yarn is less likely to fall of them by accident (their smoothness are relative to how fine their varnish is and has been polished);
Metal needles are very smooth and slick, which means the yarn slides more easily on them, and can be more sharp at the end (because metal can be shaped more easily and is much harder);
Plastic are about between wood and metal in smoothness;
Carbon needles are quite smooth, they usually have metal tips.

You can find whole sets of wooden knitting needles for less than $5. They are fine for beginners, mostly because they are cheap, and will give you an idea of what you like and dislike in needles.
For example, I love knitting with metal needles, because they can be more sharp, which helps a lot for fine lace work, and the yarn slides more smoothly on them and you can knit faster. A good friend of mine hates metal needles because they are cold and it hurts her fingers.
But all of this does not really matter. A beginner needs to begin, so, a beginner will get a ball of yarn, and read the label to know what size of needles they need for this. They will then get a pair of needles of that size and learn how to do a slip knot, a knit stitch, a purl stitch, and they will be on their way.
Now, as per why this does not really matter, well, everyone knits differently. I see it in every class I teach. I always have all my students do the same thing: cast on 15 stitches, do a few rows of knit stitch (which is called garter stitch), and then alternate knit rows and purl rows (giving you stockinette), and while they are all doing the same number of stitches, and rows, their little knitted pieces are all of different sizes. This is because we all hold our needles and yarn differently, we all have a different tension on the yarn, and in the end, our stitches are not all of the same size.
A loose knitter will not be able to knit using metal needles because the stitches will keep falling off, since their knitting is very loose. They will often prefer wooden needles, because they are less smooth, and the stitches are less likely to fall off.
A tight knitter, on the other hand, will have a hard time using wooden needles because the stitches will not want to move easily on the needles, and they will be forced to slide their stitches so that they can continue knitting. They will most likely prefer metal or carbon needles.