When to buy baby things is up to you. Some people will start right away so they spread the expense out over several pay checks. First time around I bought 1-2 packs of diapers every week so by the time baby showed up I didnt have to buy diapers for the first year. Also a lot of people will wait to buy things after their baby shower so that way they dont buy double or end up with more then they need.
I'm so sorry for your loss. But, congrats on your new little bundle. You should buy whatever you want when you feel up to it. Don't be discouraged. I didn't buy stuff until I was 30 weeks and I wish I would have sooner bc by that time i was so uncomfortable I couldn't enjoy the purchases.
I think the diapers with the umbilical cut out are awesome so buy those. :)
Also, you'll need a car seat carrier. They put your baby in it for an hour to make sure they can handle the car ride home. Get a take home outfit that is for a premie bc he's going to be really tiny.
Your going to be fine! Best of luck!