when someone says they are "new to photography" that's a relative thing. But since you asked about the 50mm lens that people talk about a lot, it's because it's been a standard focal length for as long as 35mm cameras have been popular and as a "prime" lens (not a zoom) it will let in more light as most primes do (virtually all).
This is very helpful in low light, but if you are going to have your first child you will want to get a lot of photos (babies change almost daily). And while a lens that lets in more light than the zoom you most likely got with your camera (18-55) the "nifty fifty" even though it will let in much more light still (in most cases) will not be adequate when used indoors. The 18-55 has "IS" or "image stabilization" which helps but not as much as the "faster" "nifty fifty" -
The only sure way to get great exposures without a lot more equipment (especially if the baby is not asleep) is to buy a Canon brand EX flash - Babies don't like bright lights but with an EX flash you can bounce the light off the ceiling or even off the wall behind you and (unless you are living in an airplane hanger) you should get perfect flash exposures without getting the flash in the babies eyes - he or she probably won't even notice it - but in a normal size room it's more than enough light to get good (very good) exposures. The flash is very bright, but the duration is around 1/1000th of a second, so when bounced it isn't something that will be upsetting to a baby (or cause "red eye") -
Do as much reading as you can and start off with simple settings. Once the flash is attached you are somewhat limited to aperture and completely limited to shutter speed so don't let others make you feel "inadequate" by using the Auto mode or the "P" mode - they both work exceptionally well with flash and there is no reason to make things more complicated than they need to be.
As you progress you can learn to do all kinds of things using flash (as well as natural light) but as someone completely new to photograph - or even just new to a digital SLR camera, don't rush to do things the hard way....you will figure out and learn from reading and from trial and error how to use the more complicated settings but it's not worth missing those newborn shots that you only get to take for a VERY short time.
Babies grow up much faster than adults learn photography - so don't try to get ahead of yourself.
As for the 50mm "nifty fifty" it would certainly let you get better portraits of your wife, friends and family than the 18-55 kit lens, but even though you will have the baby outdoors and not need the flash - most of a newborn's time is spent indoors (almost all of it for the first month or so) - and without good lighting and a very fast lens and a tripod ....start with a flash - it's something you will always be able to use even is you "upgrade" over time to new camera bodies and better lenses. Same with a tripod....but they are used less and cost far more for the amount of use they get from beginners. By the time you really feel the need for a tripod you will want one that will last you a lifetime. So those are expensive (if money is an object - which it becomes for most people when they become parents).
If you get a flash be sure it will work as a bounce flash - and do NOT think that the built-in flash has any value...that's fine for emergencies or a quick snapshot of your table in a restaurant, but you will want at least an EX flash that can tilt and swivel...I am not up on the newer models, but you can't go wrong with the 430 EX II which is a flash that will be compatible with other Canon flashes if (or when) you get involved in multiple flash photography.
Edit: I see while I was typing that you got other suggestions to get a flash. It's really a "must have" accessory. I had mentioned that you could take photos outdoors without a flash but the truth is (at least in my case -and I have been a photographer for far longer than anyone having a baby now is likely to have been alive) I virtually ALWAYS use a flash even when shooting in bright sunlight (to fill in harsh shadows if taking pictures of people) - Pretty much the only time I don't use flash is shooting objects that are very far away with a long telephoto lens (birds in flight - outdoor sporting events, landscapes, etc.) -
I don't know why you would need a vertical grip Unless you think it just "looks cool" - but it won't do anything at all to improve your results. Just makes the camera look bigger. They hold two batteries but you can carry a second battery in a pocket and it won't take up any real room. Too many brands - ask the owners of 20 different grips which is the "best" and other than those who say they'd rather have a Canon grip - there isn't much difference - they are all clones of the Canon grip so they look and work identically. (I once had a Zeikos grip and thougt it was great).