OK. Here's me being totally brutal. We've been on a pretty tight budget as you can imagine having to buy two of everything. Here's things on the lists already posted that I think you DON'T need!
Moses basket/crib - they only last a few weeks and a cotbed does just as well and has a longer life.
Bouncer - not sure if door bouncer or chair bouncer was meant. I wouldn't get one straight away. Assess whether you want a door bouncer later on. For instance, I would get one for Tom because he's really into standing up but I know Charlotte wouldn't be fussed about it. Chair bouncers, they've only really started being comfortable in them in the last few weeks (no idea why). A lot of people I know bought their children those bumbo seats instead as they can now hold themselves upright.
Creams/powder/shampoo. - you don't need these as you can wash the baby in water only and they barely have any hair at birth (usually). We started using bubble bath when they were a couple of months old although that was more for our benefit than theirs. We use a body lotion for a nice massage for them after the bath, but I wouldn't say it's essential. Even now, we don't use any shampoo and baby powder is not meant to be great for little lungs and my antenatal classes advised against it.
Room thermometers you can get free from all sorts of places and some monitors have thermometers built into them.
Breast pads - you may not need. See how it goes and get them afterwards.
Muslins - never used. Back to my suggestions of a load of cheap towels (Wobbles!)
Bath seat - you don't need. In fact they seem happier having the freedom to splash about.
Bath thermometers - we got one with our baby bath, but you don't really need one of those either. You could bath them in the basin at first if you didn't want to bath them in the big bath early on. Sponge supports aren't that great either. We have a couple but they still slide about on them. My Mum got me a bath mat from Morrisons for a quid and that does the trick.
Changing unit - you don't need. We change them on the floor on a change mat which is a lot safer when they are rolling all over (they seem to enjoy the kick about without nappies on) though it does kinda do your back in!
Sling - it was handy for a while when they were smaller but I barely use it now.
Gripe water - not used though I think we had infacol given which does the same but we didn't really need it. That said, if you do need it you can guarantee that it will be late at night when the chemist is shut!
Cot bumpers - you can't use until the baby can roll over so I'd wait and see if you want them or not.
Nursing chair - nice to have but not essential. Once you get the nack you can breastfeed anywhere even walking around!
I hope no-one sees this as critical of what you have already suggested but if you are really wanting to do this on a budget there are things that you don't
really need.
Must go do a post in the for sale section of slings, bath sponges, etc.