We don't wash mid week - we do the uniform wash on Fri night/Sat morning, so this is based on that:
A complete set of jumper, polo shirt, trousers and socks for each day (except PE day).
A complete spare set, plus pants & socks that is kept in her bag (school request this, but to be honest even if they didn't I'd still include it as at least once a week she seems to soak her sleeve ends or socks to the point of needing fresh during the day)
A complete PE kit set: school logo hoodie, house colour T-shirt, jogging bottoms, trainer socks, trainers.
A pair of PE shorts for the warmer months
A school logo jumper, plus white polo shirt that is kept in the drawer and only worn on school photo days (we have these twice a year, and I bought the jumper slightly big and it's done 2 academic years, plus will do her younger sister).
Most of our stuff is non-logo, however the logo stuff we get from the school's PTFA second-hand uniform sales. Now this will differ for every school, but the second-hand stuff for us is nearly new condition and a total bargain.
We got the school coat second-hand as the PTFA were selling them off super cheap - £3/£5 - some still had tags on!!! I wouldn't have bought it at full price from the uniform shop though, as she already had a waterproof coat. Our school one is really good quality though and nice and warm.
I'd also say, that if your school is like ours and has different coloured options for polo shirts go for the dark colour over white - ours are royal blue or white - as it wears better, but get a white one for photos as imo it looks nicer against the jumper (also royal blue)
If you made it this far, to summarise my advice would be:
6 polo shirts (1 for photos)
5 jumpers
1 logo jumper for photos (second hand)
5 trousers
1 PE hoodie (second hand)
1 PE t-shirt
1 jogging bottoms
1 shorts
1 trainers
6 socks
1 trainer socks
A warm waterproof coat of some kind - school one if its a bargain