50mm is fine. Get in close, keep back grounds as simple as possible, preferably a plain blanket of similar. like most portriats, focus on the eyes for head shots. Use natural light, and take/make a reflector for some fill. Also use the wide open end of the lens to do some detail shots of hands and feet, which are very popular and will remind family how tiny they were.
Most of all, relax, take as many shots as you need to, have loads of patience, babies will not always perform the way you want, but give them time and yoy should get a nice mix of shots
fwiw, these were taken in a tiny bedroom with a tiddly window, on the parents bed. Baby is 2 weeks old, a plain white blanket and a very cheap net curtain to hide nappy [we tried sans nappy, but he kept ...err...making a mess

]
if my photos turn out half as good as these ill be well pleased
these were with a 24-70 f2.8 but a 50mm would have been better tbh, but I dont have one
edit: should also say, if little one is sleeping, you might be able to get the classic dad holding naked baby tummy down in hands shot...or other such stuff. Also, shots of parents gently kissing baby on head are often appreciated