# 9 corks are the way to go when using a floor corker/bench corker. They're a larger diameter than # 8's & are suitable for long term aging/cellaring. Natural or synthetic, whicheaver you prefer.
# 8 corks are a smaller diameter & are more suited to use with plunger/hand corkers as they're easier to get into the bottles. They are not so good for long term cellaring, but they're reportedly fine for 2 yrs or less.
# 7 corks are NOT for use in 750ml bottles. They're for beer bottles (think lambic style with cap & cork).
Hope this info helps.
Regards, GF.