One of mine was an October baby and 2 others middle of winter babies. I only found a pramsuit good if you were going out for a long walk. I found a medium weight jacket, hat and a couple of folded blankets easier whenever we were going in and out of the car/ houses/shops. If they are sleeping you don't want to lift them out of a car seat/pram immediately when you go inside to get the pramsuit off and I found unless outside they can get very warm in a pramsuit. But with layers you could take off a hat, lift off a blanket and unzip a coat whilst they remained asleep.
Mine would have always worn short sleeved vests and sleepsuits. You can't have too many of these. Don't buy too many newborn size as one of mine was 9lbs 12.5ozs and fitted newborn clothes for a week! Buy more 0-3 months size.
If your main change mat is upstairs I found it handy to have a mat and basket of essentials e.g. Nappy, wipes, spare vest, sleepsuit etc downstairs to save you always running upstairs.
A sling - can be worn inside the house to get things done whilst holding an unsettled baby close.
A pack of 10 terry nappies - not to use as a nappy - but as a burp cloth, under their head when lying on a play mat to catch any milk dribbles, under their bums if having nappy free time, on the changemat as the plastic can feel cold to lie a baby on in the middle of the night etc etc.
Grobags - if you are going to use them. TKMaxx often have them at good prices.
One of my winter babies didn't like cotton cot sheets they only liked the flannelette sheets as they didn't feel as cool to the touch.
Happy shopping!