Crochet baby blankets, they pop up every time someone has a baby. I have nothing against them. I even make a few every year for people. I also get into discussions about what patterns and what yarns to use in them with the people asking for them and people asking my opinion about a particular yarn and/or a particular pattern.
So now I’m going to write my personal recommendations on the subject. These are my personal views, and I know there are others who think otherwise, but these are what I use for baby blankets, based on my own experiences and research on the subject.
The yarn you use is, to me, the most important part of the blanket. Overall, acrylic yarn is the number one type of yarn recommended for newborns, though there are others. Natural animal-based fibers, like wool, can cause allergic reactions in newborns. Newborns have very sensitive skin and can find wool more scratchy and itchy than softer yarns.
Softer yarns, besides acrylic, include cotton and bamboo. Cotton and bamboo are plant-based natural fiber yarns. I, personally, use Caron One Pound yards, but if you’re really unsure what to use, look for a yarn that has baby in the name. These yarns are specifically made for baby related items. If you can’t find any of those, use the softest yarn you can find.
The pattern you choose also requires some thought. You want a pattern that doesn’t contain large holes, like the a Granny Square, or a Virus Pattern Blanket. I am aware that there are pattern books that provide fillet patterns and granny chevron baby blanket patterns. I don’t use these patterns as I’ve had babies get tangled in the hole of the patterns to the point that the blankets had to be cut up to prevent damage to the baby. If you do choose on of these patterns, I strongly urge you not to leave the baby alone with the blanket until you are sure them can get themselves untangled from it.
My go-to patterns for baby blankets is a chevron pattern that uses single stitches and half-double crochet stitches. As you can see from the photo below, the holes are much smaller and its stitch work is much tighter, meaning is will be warm, and yet still soft enough for a newborn. It will also last a long time as there is less risk of it getting caught on something and ripped.

There are hundreds of patterns to choose from, a simple internet search will bring them to you. Look at them and choose one that you feel is appropriate for the baby you are making, or requesting, a blanket for.