You don't say what sort of role but I think you are perhaps worrying a bit too much. It is business casual not an episode of suits.
It is likely men will be wearing trousers, shoes, and a shirt with no tie. Probably a coat but no jacket or a blazer depending upon their day and the weather.
Women are harder to predict, I would guess quite a range but lots of dresses, no jeans or trainers.
We have switched to dress for your day now but when we were business casual most women wore a dress (no jacket), or trousers/skirt and blouse or top.
Suits and jackets tended to only be for meetings. Plenty wore flat shoes rather than court shoes.
I wouldn't buy much yet, just enough for the first week and go for reasonably smart. Then when you see how people dress you can buy more that fits the general mood, if you have gone too smart it will have given a good impression and you can use the outfits for meetings and smarter days.
My advice would be to get your colours done (it isn't expensive, look at style me happy). It helps you avoid buying things that don't suit you and helps you buy things that complement each other. It is especially good if your confidence is low.
Then I would buy one nice jacket in a neutral colour (or use the one you have) two pairs of trousers one pair to match the jacket and one to contrast. Three tops, and a couple of dresses that complement the jacket. One pair of loafers. Then mix and match for the first week.
While you are searching bookmark a few more bits to order when you have a better feel for things.
If you have a smart handbag not big enough for a laptop use that or borrow something. You will probably be given a bag with the laptop if you are expected to take it home. At my job most people use these and either no bag or a smaller bag. Unless you love handbags there's no point buying a lap top bag if you don't need to.
Look at M&S they have decent workwear, especially the autograph range. Our senior partner wore an M&S dress to our AGM. Not high fashion but entirely acceptable and affordable. Boden is good for workwear. Then look for more expensive stuff like hobbs or whistles secondhand.