I'm pregnant with my second, but all our baby stuff is back in the UK, so I'm buying almost everything second hand. This is what I consider essential:
Buggy
Baby-wearing device
10 long sleeved bodysuits, up to 1 month size (it'll be winter here)
6 sleepsuits, up to 1 month (this is probably not enough)
Hat
Snowsuit (again, winter here)
Ikea shoe sorter thing for storing small clothes in our own wardrobe (it's about a tenner and fantastic)
Chicco next to me crib (second hand off Gumtree)
New mattress for the crib (parents generously bought this, shamefully I might not have bothered as the second hand one had only been used twice)
Two sheets for crib
Waterproof mattress protector for crib
Two swaddles (not technically necessary but I will do anything if it might get me more sleep)
Two sleeping bags
Self-rocking chair thing (second hand off Gumtree; wouldn't have bothered if it hadn't been so cheap but it was useful to have last time)
Breast pump bundle with bottles etc (second hand off Gumtree; total bargain)
Things I'm not buying:
Blanket - we have a fleecey throw that will be fine
Baby towels - gave up using these last time, they're tiny!
Changing mats - I may live to regret this, but we have towels etc
Changing table - good grief, why do people throw their money away?!
Car seat - we've no car...
Toys - there is no need whatsoever for the first six months according to my son
Baby gym - I did use it last time, but meh, we'll cope without
Muslins - we have a few knackered t-shirts that I'm happy to cut up
Ewan the Dream Sheep - you let me down, Ewan! I had all my hopes pinned on you!
I'm definitely at the more extreme end, but we might be heading home soon after the birth so I don't want to waste money. I hope this helps!