That sounds like plenty of nappies to start with. I will say that, depending on the size of your newborn, you may find them all a little big. My DS was a pretty small newborn (6lbs14oz but 55cm so the dimensions of a 5.5lbs baby in the middle) and terry nappies, infant prefolds (like the Bambino Mios) and small wraps didn't come close to fitting him for the two months. The good news is that muslins make a great newborn nappy and you'll want to have plenty of those in anyway. Check out this video:
Even if you have a more average size (8lb) baby, muslins might be the way forward for the first 4 weeks. You may also find that you need some more xs wraps but you could wait and see what size/shape baby is first.
I think that it's a good idea to have disposables for the first couple of days, just until the meconium passes, but then you can go straight on to cloth. I'd get on to cloth while you have support at home to help get you started. If you have a OH try and get them really into cloth nappies too. I found DH's support invaluable; using YouTube vids he learnt how to fasten a prefold and a muslin with nappy nippas before I did and so he did all of the nappy changes while he was at home - a massive help as it let me focus on breastfeeding and I think it made DH feel like he had a real role to play.
Thinking back, I think that we did continue to use disposables at night for the first week, week and a half, until we became good enough at cloth to do it with bleary 3am eyes. As you end up changing 10-12 nappies a day, by the end of day two you're an expert, no matter what type of nappy you choose.
As for how long they will last, it really depends on the size and shape of your baby but you're going to need bigger wraps for sure when the baby is 3-4 months old. The terries could last for a good long while, although you may find that you need boosters eventually.
Using cloth is a steep learning curve for sure, but then everything about having a newborn is! In my opinion it's completely worth it. I have a 2.7 year old still in cloth (although about to finish with them very soon - I hope!) and a newborn due any day to take over the stash.
Feel free to ask anything else - I could clearly talk about cloth nappies all day 