My baby is 5 months old. This is what we have/use:
top and tail bath - Got given 2, never used either, they have become useful storage!
baby bath (and newborn insert) - Again got given a baby bath. I tried to use it once and DS screamed the house down. Also too big and heavy when full of water, a pain to fill! Had a plug so easy to empty though. We now use it as a basket to carry things from room to room! We have the insert but never used it really. DS hates any form of bath unless he is in with his Dad anyway!
cotton wool - Very useful, but watch out if you have cats, they love to shred it! I also found I used (very wet) cotton wool on myself post-partum to gently clean blood from sore bits a few times a day.
cotton pads - Useful but cotton wool is sufficient, and cheaper. I found cotton wool balls the best - the pleats were a bit of a faff.
sudocreme - I have never used it, but you get a small free sample in your Bounty pack anyway.
a baby hair brush and baby nail cutters - Both bought after a few weeks. DS had hair but not all babies do. The nail cutters I found useful but for the first few weeks just used my teeth.
nappies - Obviously
towels - We have 2 small hooded towels and honestly I don't find the hoods have any use other than for cute photos! It is useful to have small towels just for baby though.
flannel clothes - The ones which go over your hand like a glove are good but you don't really need them - you can wash with your hands.
sponges - Seem a bit pointless to me. Baby likes to suck on them though!
hooded towels - See above.
Other stuff we use:
Baby wipes - I know, I know - and in fact I wouldn't recommend getting them before the baby is born, but some kind of cloth to wipe bums with is so much simpler than faffing around with cotton wool when they have done a huge explosive poo. I did start off using cotton wool + water, and then when DS did a giant poo I would use one movement with a baby wipe to get most of the poo off and then go over with cotton wool + water for all the creases. Actually I found warm water more effective on sticky meconium/dried on poo than baby wipes.
Muslin cloths - Get at least a dozen and secrete two or three in easy to grab places in every room of the house. They are invaluable for wiping up sick, poo, dribble... everything!
Cotton nappies - prefolds and terry or cotton squares, I got some from freecycle and although I don't use them as nappies, they are fab as changing mats, sick cloths, nappy free time, bum wipes! Also I found if DS weed or I leaked milk on the bed, I could put one of these over the damp patch and go back to sleep without having to change the whole sheet. (Although having said that, we also have a waterproof matress cover on which has been brilliant in protecting the matress from everything)
Old towels - For nappy-free time, which seems to reduce nappy rash, and babies love it at about 3-4 months when they are just starting to roll and/or find their feet to play with. And also to sleep on in the first days after birth (if you come home very soon or have a home birth - I came home the same day)
Weleda Calendula Nappy Change Cream - Alternative to sudocrem. Smells much nicer and works very well - a little goes a long way. I got a free sample which I think was from sending off a flier I picked up at the Baby Show. I don't use it as a barrier cream, just if he has any redness.