Here's an edited version of a list i did for friend recently. Obviously our situation may be different to yours (though also had a winter baby).
Sleeping:
Crib upstairs and Something to sleep in downstairs ? we used a travel cot with bassinet. Could also use a moses basket or carry cot but I thought the travel cot was better value as you can carry on using it ? as a travel cot (duh!) and as a play pen. We also used a small pop up travel cot which was great for staying away from home and camping.
Bedding. I found sheets and cellular blankets were best for the first few months as they give you more flexible temperature control, but after that grobags are definitely the way to go ? you can get them in them ready for bed and put them straight down, and they can?t kick them off.
Didn't find we needed a monitor until a few months on as ds was generally on or near me constantly.
Changing:
We didn't have one but you may want a changing table if having a cs so you don't have to bend.
Changing bag. We just used an old tote bag that doubles up as my handbag. In said bag we have the following:
? Nappies
? Changing mat (portable, washable plus spare)
? Barrier cream (highly recommend Neal?s Yard Baby Barrier Cream ? it?s expensive but lasts ages and is really good)
? Bags for disposal ? we just use cheap supermarket nappy bags (or put them straight in the outside bin if at home).
? Hand sanitiser ? for al fresco nappy changes where no handwashing is available.
Bath:
You only need a baby bath if (like us at the time) you don?t have a bath. Otherwise maybe some kind of support for a big bath.
Baby towels aren?t necessary but nice. You really don?t need any toiletries unless you really want them ? I just used a bit of olive oil for baby massage. For fingernails I just used my teeth!
Transport:
Car seat and baby carrier or sling. This was invaluable just for doing stuff around the house and was much less hassle for going out than a pushchair - we live in the middle of nowhere though and a pram would have been useless for us. Re pram/pushchair I would say that unless you have masses of storage space get something that folds up fairly small.
Feeding:
If you are bf all you need is breast pads, some nipple cream (big thumbs up for lansinoh), a good feeding cushion, and maybe a pump - wait and see what you need though (shops will still be open!) - I preferred a manual pump, but didn't need one for a few months. Muslins.
Other stuff:
Clothes. All you need is vests, sleepsuits (preferably with scratch mitts built in), cardies/jackets, hats and a pramsuit or snowsuit. Outfits are cute put are a pain to put on and keep on, and you will be changing clothes several times a day. Also, most of their time is spent sleeping so it easier if they are already dressed for it. Shoes are frankly bonkers at this stage. Just go for basics and a few nice things for showing him off in ? I was horrified how many things we had went totally unworn.
Other stuff like bouncy chair, baby gym were really good, but you won't need them straight away.
Sorry if a bit long winded!