What is your budget? You can buy a lot of STUFF for baby or you can remember that pioneer women raised them on the praire with some cloth for diapers and their breastmilk.
NEEDED:
1) A Peditrician. If you don't have one now start calling. Once you find one, ask about:
2) Baby Tylenol
3 ) Baby Cold Medicine
4) Diapers, wipes (though rags works), diaper rash ointment (we used Desitin)
5) Somewhere for baby to sleep. If you want them to sleep in your room, a pack and play with a bassenett attachment is flexible.
6) A changing surface - you can use the floor. We used an old desk in the living room and the tops of the dressers in the family room.
7) Something to feed baby (formula and/or breastmilk - I'm a fan of having a can of formula just in case regardless, a lot of breastfeeding advocates don't like this idea).
7a) If you feed formula, you'll want bottles, nipples and a bottle washer.
8) Things for baby to wear. A summer baby can get by in two dozen onsies - a winter baby may need a few fleece sleepsacks and far more clothes. Of course, you'll WANT a lot of cute little outfits, too.
9) CARSEAT
That's it.
For you:
1) The biggest bag of the biggest maxipads you can find
2) A jar of Tucks
3) A box of kleenex and chocolate to help the hormones work their way out.
You'll want something to carry baby in - a stroller and/or a sling. I was actually neither a stroller mom, nor a sling mom - I had an inexpensive stroller - and an umbrella stroller - after the infant stage we used the $11 umbrella stroller.
Baby swings are nice to have from day one. You could also get a bouncy seat. Personally, I don't think you NEED both if you are on a budget.
High chairs and exerscaucers are nice - but you won't need either for a few months. Exerscaucers are a lifesaver, but have a limited life - if you can borrow one from a friend, I'd recommend that, they can go through a few kids pretty easily.
The door jumpy things - some kids love them, some don't - once again, limited life - find a friend whose baby is outgrowing it. Also, they don't work in all houses.
Neither of my kids was at all interested in baby toys - like the activity mats or gyms or any of that. You'll get some of it, but wait for it to arrive rather than go buy it.
You won't need a highchair for a few months.