Things that I found invaluable in those first few months, although I had a winter baby so Ill do the summer version!
Zinc cream for bottom
A nappy bag with a nappy clutch (a foldable fabric bit that contains nappies and wipes)
Cetaphil cream for baby eczema
Infants friend for wind (some people don't think it works but I think it helped us)
Wraps - you would use muslim.
Basic bedding - cotton sheets and blankets
A whole bunch of face cloths which can be used for bathing, burping, etc
Onesies - a whole bunch in different sizes, starting from 0000
A hat and baby suncream for summer
A few nice outfits in different sizes
Socks and singlets
Capsule that slots into the pram - a lifesaver!
A head brace for the capsule
A lamp with a very dim bulb for evening breastfeeds (I have the lowest wattage and still put a sarong over the lamp)
Books and DVDs for the marathon breastfeeding sessions
Lanolin for your nipples
Nursing bras and tops
Washable breast pads
A soft mat or rug for tummy time
Some simple toys that are colourful for baby to look at
I also found Rescue Remedy to be great for myself when baby wouldn't settle or my hormones were playing up.
A bubba moe sling to allow fussy baby to sleep.
A hugabub for the same purpose above - one would work better than the other sometimes.
An electric swing - to help baby settle and when I needed a break from holding her.
A fan for her room (for summer).
When she was not a newborn we used a Love to Swaddle sleep sack thing - it allowed her to suck on her hands while we helped her learn to self soothe.
Despite what the PP said about not needing to express, I had to. I had low supply and was on that breast pump from the start. Could be handy to have if you're considering breastfeeding anyway. In which case, have about six bottles and teats (which will be enough to cover a day of feeds later on if moving on from BF or it doesn't work out.) Buy the larger size bottles, no point in buying the small ones, just means you'll have to buy larger ones later. You'll also need a bottle brush and breast milk storage bags or trays.
Now that my DD is a bit older (almost 7 months) the things I find invaluable (not including the bedding and clothing which is the same as above) are generally the things that keep her active self occupied when I need to do something. That is, the gadgets that keep her in the one (safe!) place!
A good quality bouncer - we have the baby bjorn bouncer which is expensive but we use it multiple times a day if we need to put DD down somewhere safe, we've taken it to the beach, to cafes etc
A play gym with a variety of hanging toys.
Simple toys to play with - fabric blocks, baby books, rattles, soft toys, teething rings
A jolly jumper
A fisher price jumperoo (she LOVES this!)
A selection of bedtime stories
A bumbo with a tray (we use this instead of a high chair too at the moment)
An ergo carrier
When you start solids, assuming you're not doing baby led weaning (look it up for later!) you'll need:
Something to feed baby in (high chair or bumbo)
Lots of face washers
A device to puree food with.
Storage containers or ice cube trays and freezer bags
A sippy cup
For winter just rug up your LO with lots of layers and use a sleeping bag. We use Bambino Merino sleeping bags and they're great - expensive but can be used up to two years of age. We also live in a very cold area and use lots of layers of clothing and heat the room with an electric oil heater - you can't swaddle once they roll over or use any bedding at this point in case of suffocation.
Anyway I hope that helped you! This is basically all I use on a day to day basis - these are the things that I find wonderful!
Edited to add some things!
Edited by axiomae, 09 January 2013 - 07:36 PM.