There was a wonderful book out which I relied heavily on (along with my sister), I'm trying to remember the book title (if you tell it or the authors to me, I'll be able to say nope or yes it's that one!)
Something like Baby Bargains... it was a tall narrow thick book and sort of a consumer guide/girlfriends guide rolled in one, answering your exact question, along with quality and which products in that category were good/overpriced/junk/etc (rating sheets).
You truly do not need everything. Borrow, buy used/second hand (not car seats, of course but pretty much all else), shop on craigs list/garage sales, etc. Freecycle.org is another wonderful resource (cant be too picky there but it's great as everything is free).
Back to the book, the authors (a husband/wife couple) wrote this book and also one for brides (which I never saw). Look for it at the library (may have to look online and put in a request to get it, as it's not going to just sit on the shelf!!!). Again, it is a tall narrow thick book. About the size of a business envelope, but about 1" thick or more. (but my son is now almost 7 so they could've changed since then.) It is a WEALTH of information. I repeatedly checked it out from the library and loved it!
And even then, you do not need to get everything they recommend, it is what you personally feel is a must. And then there are personal variations. For example, I loved my boppy pillow for nursing but if you're not gonna nurse, or if you are quite large or if you have lots of pillows laying around and/or always nurse in the bedroom or a sofa with arms, then the boppy is a space (and money) waster.
Anyway - my "musts": baby washcloths, onesies, socks that DO NOT SLIP OFF (Old Navy worked for my toddler but I dont remember the brand I used for my baby), a swing or baby seat (I had the FP infant seat that converts into a toddler rocking chair - loved it! Still keeping that on hand for visiting babies). A pack n play (again, keeping that on hand).
Exersaucer (used or borrowed). They now have bumbo?? chairs for babies that "must" sit but can't quite yet, wasn't out when my son was a baby. I am not sure how I feel about that. I saw a friend's baby who did not want to recline, but wanted to sit up and watch what we were doing and we had to be working at the table and cldnt hold her, so she got that seat and baby was happy! So for that, for short times, sure.
Toys, really, all you really need is a set of links up till about one year old, then expand with a few classic toys like shape sorters, etc. Get quality toys over quantity!!! And washable ones! A few good books, after that go to the library!!
Never mind all the videos and such -if you must watch them, check them out from the library! (Signing Time is a great one for older toddlers & up tho). You do NOT need the whole set of baby einsteins, just one or two (again, 2nd hand is FINE.)
A stroller and a baby carrier (I loved my bjorn). I did not have a travel system, but did have a base for baby seat to snap into in the car.
A safe place for baby to sleep, clothes to wear, diapers to contain blowouts, wipes (there's a great recipe to make your own wipes out of plain white Bounty paper towels, love this!!) shampoo (I love Target's brand of J&J baby shampoo), blankets (of various sizes and light weight, some a little thicker, depending on season & purpose) and really, that is all you need. :-)
Pack n play - we picked a nice one that had a basinet and changing table attachment, with curved ends. I was sorry I picked that, as I would've much preferred straight edge ends (my arms are short and it was HARD to tuck in the sheet/blanket on the bottom) and I almost never used the attachments. Waste of $$ (I had 3/4 bassinet not a full bassinet, so I dont know if it would've been more used had it been a full sized bassinet.)